Search

The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by the associated Arens–Eells space, along with the duality between M and the metric dual space M # defined by the real-valued Lipschitz functions on M. However, alternative approaches to measuring distances between sequences of elements of metric spaces (essentially involved in the definition of p-summability) exist. One approach involves considering specific subsets of the unit ball of M # for computing the distances between sequences, such as the real Lipschitz functions derived from evaluating the difference in the values of the metric from two points to a fixed point. We introduce new notions of summability for Lipschitz operators involving such functions, which are characterized by integral dominations for those operators. To show the applicability of our results, in the last part of this paper, we use the theoretical tools obtained in the first part to analyze metric graphs. In particular, we show new results on the behavior of numerical indices defined on these graphs satisfying certain conditions of summability and symmetry. [ABSTRACT FROM AUTHOR]

Introduction. Open Government is a form of public policy based on the pillars of collaboration and citizen participation, transparency and the right of access to public information. With the help of information and communication technologies, governments and administrations carry out open data initiatives, making reusable datasets available to all citizens. The academic community, highly qualified personnel, can become potential reusers of this data, which would lead to its use for scientific research, generating knowledge, and for teaching, improving the training of university students and promoting the reuse of open data in the future. Method. This study was developed using a quantitative research methodology (survey), which was distributed by email in one context block and six technical blocks, with a total of 30 questions. The data collection period was between 15 March and 10 May 2021. Analysis. The data obtained through this quantitative methodology were processed, normalised, and analysed. Results. A total of 783 responses were obtained, from 34 Spanish provinces. The researchers come from 47 Spanish universities and 21 research centres, and 19 research areas of the State Research Agency are represented. In addition, a platform was developed with the data for the purpose of visualising the results of the survey. Conclusions. The sample thus obtained is representative and the conclusions can be extrapolated to the rest of the Spanish university teaching staff. In terms of gender, the study is balanced between men and women (41.76% W vs. 56.58% M). In general, researchers responding to the survey know what open data is (79.31%) but only 50.57% reuse open data. The main conclusion is that open government data prove to be useful sources of information for science, especially in areas such as Social Sciences, Industrial Production, Engineering and Engineering for Society, Information and Communication Technologies, Economics and Environmental Sciences. [ABSTRACT FROM AUTHOR]

Consider a finite directed graph without cycles in which the arrows are weighted by positive weights. We present an algorithm for the computation of a new distance, called path-length-weighted distance, which has proven useful for graph analysis in the context of fraud detection. The idea is that the new distance explicitly takes into account the size of the paths in the calculations. It has the distinct characteristic that, when calculated along the same path, it may result in a shorter distance between far-apart vertices than between adjacent ones. This property can be particularly useful for modeling scenarios where the connections between vertices are obscured by numerous intermediate vertices, such as in cases of financial fraud. For example, to hide dirty money from financial authorities, fraudsters often use multiple institutions, banks, and intermediaries between the source of the money and its final recipient. Our distance would serve to make such situations explicit. Thus, although our algorithm is based on arguments similar to those at work for the Bellman–Ford and Dijkstra methods, it is in fact essentially different, since the calculation formula contains a weight that explicitly depends on the number of intermediate vertices. This fact totally conditions the algorithm, because longer paths could provide shorter distances—contrary to the classical algorithms mentioned above. We lay out the appropriate framework for its computation, showing the constraints and requirements for its use, along with some illustrative examples. [ABSTRACT FROM AUTHOR]

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function ϕ. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modeling of livability indices in North American cities. [ABSTRACT FROM AUTHOR]

Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the n-dimensional case, such a map can be represented as a vector of size n of real-valued functions of one variable. In this paper we develop a method to approximate almost diagonal maps by means of lattice Lipschitz operators. The proposed technique is based on the approximation properties and error bounds obtained for these operators, together with a pointwise version of the interpolation of McShane and Whitney extension maps that can be applied to almost diagonal functions. In order to get the desired approximation, it is necessary to previously obtain an approximation to the set of eigenvectors of the original function. We focus on the explicit computation of error formulas and on illustrative examples to present our construction. [ABSTRACT FROM AUTHOR]

The axioms of symmetry and indiscernibility of a metric function can be eliminated and still define a topological space with good enough properties. However, among all the axioms that constitute the notion of a metric, the subadditivity or triangular inequality is the one that has been more difficult to relax. Even so, and due to the potential applications in other fields such as Artificial Intelligence, several efforts have been made in this direction. The notion of quasi-Banach space or the notion of b-metric space, are examples of structures where the subadditivity has been replaced by a weaker inequality. Following this line, in this paper we consider the non-symmetric version of the so called strong b-metric spaces. We focus our attention on the possibility of extending semi-Lipschitz maps, and still preserve (a uniform multiple of) the Lipschitz constant. As our main result, we prove that the possibility of obtaining such extensions characterizes the spaces satisfying the proposed weak versions of the triangular inequality. We also show how our results can be applied in Machine Learning to solve some technical issues, in particular, some problems related to the extension of Lipschitz functions with respect to the cosine distance. [ABSTRACT FROM AUTHOR]

We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (p-convexity, p-concavity, p-regularity) or, equivalently, some types of summability conditions (for example, when the terms of the terms in the sums in the range of the operator are restricted to the interval [ − 1 , 1 ] ) can be studied by adapting the classical analytical techniques of the summability of operators on Banach lattices, which recalls the work of Maurey. We show a technique to prove new integral dominations (equivalently, operator factorizations), which involve non-homogeneous expressions constructed by pointwise composition with Lipschitz maps. As an example, we prove a new family of integral bounds for certain operators on Lorentz spaces. [ABSTRACT FROM AUTHOR]

It is still unclear whether the density of analytic polynomials in an H-admissible space is sufficient to the minimality of the space? This question has a purely foundational background, relating fundamental concepts from the theory of H p spaces. We hypothesize that there is no general relationship between the density of analytic polynomials and the R-admissibility of an H-admissible space. We solve this problem by finding suitable counterexamples of Hardy spaces built upon some weighted Lebesgue spaces. In particular, we provide a direct construction of weights from Szegő class, which guarantees the existence of isomorphic copies of the space of bounded sequences in weighted Hardy spaces on the unit disc. [ABSTRACT FROM AUTHOR]

This work is inspired by some recent developments on the extension of Lipschitz real functions based on the minimization of the maximum value of the slopes of a reference set for this function. We propose a new method in which an integral p–average is optimized instead of its maximum value. We show that this is a particular case of a more general theoretical approach studied here, provided by measure-valued representations of the metric spaces involved, and a duality formula. For p = 2 , explicit formulas are proved, which are also shown to be a particular case of a more general class of measure-based extensions, which we call ellipsoidal measure extensions. The Lipschitz-type boundedness properties of such extensions are shown. Examples and concrete applications are also given. [ABSTRACT FROM AUTHOR]

In this paper we show that the equivalence among the classical quasi-norms of the generalized Orlicz spaces XΦ — the Orlicz quasi-norm, the Luxemburg quasi-norm and the Amemiya quasi-norm — holds under some mild conditions on the underlying quasi-Banach function space X — mainly the weak Fatou property — improving previous results of [4] for which some lattice convexity requirements for the quasi-Banach function space X were needed. [ABSTRACT FROM AUTHOR]

Taking a historical perspective, we analyze the economic growth of GAFA companies, and how they fit into the indicators that measure global human development. We explore the limits of growth -assuming that economic growth is inherent to good economic performance- by studying these cases, which are relevant insofar as they lead global economic growth in the new digital-based ("ethereal") economy. Our methodological approach contrasts the growth patterns of GAFA companies with general human growth parameters. This case-to-global study finds clear trends, suggesting that the ethereal economy is constrained only by the limits of human growth. [ABSTRACT FROM AUTHOR]

Here, we prove some general results that allow us to ensure that specific representations (as well as extensions) of certain Lipschitz operators exist, provided we have some additional information about the underlying space, in the context of what we call enriched metric spaces. In this conceptual framework, we introduce some new classes of Lipschitz operators whose definition depends on the notion of metric coordinate system, which are defined by specific dominance inequalities involving summations of distances between certain points in the space. We analyze "Pietsch Theorem inspired factorizations" through subspaces of ℓ ∞ and L 1 , which are proved to characterize when a given metric space is Lipschitz isomorphic to a metric subspace of these spaces. As an application, extension results for Lipschitz maps that are obtained by a coordinate-wise adaptation of the McShane–Whitney formulas, are also given. [ABSTRACT FROM AUTHOR]

We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The "best" indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented. [ABSTRACT FROM AUTHOR]

We study some new summability properties of multilinear operators. We introduce the concepts of φ‐summing, φ semi‐integral and φ‐dominated multilinear maps generated by Orlicz functions. We prove a variant of Pietsch's domination theorem for φ‐summing operators, providing also a characterization of φ‐dominated operators in terms of factorizations. We analyze vector‐valued inequalities associated to these maps, which are applied to obtain general variants of multiple summing operators. We also study translation invariant multilinear operators acting in products of spaces of continuous functions, proving that a factorization theorem can be obtained for them as a consequence of a suitable representation of the corresponding normalized Haar measure. [ABSTRACT FROM AUTHOR]

A new stochastic approach is presented to understand general spectral type problems for (not necessarily linear) functions between topological spaces. In order to show its potential applications, we construct the theory for the case of bilinear forms acting in couples of a Banach space and its dual. Our method consists of using integral representations of bilinear maps that satisfy particular domination properties, which is shown to be equivalent to having a certain spectral structure. Thus, we develop a measure‐based technique for the characterization of bilinear operators having a spectral representation, introducing the notion of eigenmeasure, which will become the central tool of our formalism. Specific applications are provided for operators between finite and infinite dimensional linear spaces. [ABSTRACT FROM AUTHOR]

In this paper, we describe a new trend analysis and forecasting method (Deflexor), which is intended to help inform decisions in almost any field of human social activity, including, for example, business, art and design. As a result of the combination of conceptual analysis, fuzzy mathematics and some new reinforcing learning methods, we propose an automatic procedure based on Big Data that provides an assessment of the evolution of design trends. The resulting tool can be used to study general trends in any field--depending on the data sets used--while allowing the evaluation of the future acceptance of a particular design product, becoming in this way, a new instrument for Open Innovation. The mathematical characterization of what is a semantic projection, together with the use of the theory of Lipschitz functions in metric spaces, provides a broad-spectrum predictive tool. Although the results depend on the data sets used, the periods of updating and the sources of general information, our model allows for the creation of specific tools for trend analysis in particular fields that are adaptable to different environments. [ABSTRACT FROM AUTHOR]

We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and other measure-theoretic notions are introduced. We analyze Lipschitz-type inequalities in two fundamental cases. The first concerns almost everywhere pointwise inequalities, while the second considers dominations involving integrals. These Lipschitz-type inequalities provide a suitable frame to work with operators that take values on Banach function spaces. In the last part of the paper we use some interpolation procedures to extend our study to interpolated Banach function spaces. [ABSTRACT FROM AUTHOR]

Copyright of BiD is the property of Facultat de Biblioteconomia i Documentacio, Universitat de Barcelona and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown. [ABSTRACT FROM AUTHOR]

Copyright of El Profesional de la Información is the property of EPI SCP and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the class of (p, q)-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for (p, q)-regular operators yielding new Marcinkiewicz-Zygmund type inequalities for Banach function spaces. An extension theorem for (q,∞)-regular operators defined on a subspace of Lq is also given. [ABSTRACT FROM AUTHOR]

This article shows an approach to the study of two fundamental aspects of the prepublication of scientific manuscripts in specialized repositories (arXiv). The first refers to the size of the interaction of "standard papers" in journals appearing in the Web of Science (WoS)--now Clarivate Analytics--and "non-standard papers" (manuscripts appearing in arXiv). Specifically, we analyze the citations found in the WoS to articles in arXiv. The second aspect is how publication in arXiv affects the citation count of authors. The question is whether or not prepublishing in arXiv benefits authors from the point of view of increasing their citations, or rather produces a dispersion, which would diminish the relevance of their publications in evaluation processes. Data have been collected from arXiv, the websites of the journals, Google Scholar, and WoS following a specific ad hoc procedure. The number of citations in journal articles published in WoS to preprints in arXiv is not large. We show that citation counts from regular papers and preprints using different sources (arXiv, the journal's website, WoS) give completely different results. This suggests a rather scattered picture of citations that could distort the citation count of a given article against the author's interest. However, the number of WoS references to arXiv preprints is small, minimizing this potential negative effect. [ABSTRACT FROM AUTHOR]

We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball, such as compactness and strong compactness. In con- trast with some results found in the existing literature, we show that not all right bounded asymmetric norms have compact closed balls. We also prove that there are finite dimensional asymmetric normed spaces that satisfy that the closed unit ball is compact, but not strongly compact, closing in this way an open question on the topology of finite dimensional asymmetric normed spaces. In the positive direction, we will prove that a finite dimensional asymmetric normed space is strongly locally compact if and only if it is right bounded. [ABSTRACT FROM AUTHOR]

Copyright of Anuario Think EPI is the property of EPI SCP and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in $$L^{2}[0,1]$$ by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals. [ABSTRACT FROM AUTHOR]

It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutelyp-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable stronglyp-summing multilinear operators, (p1, . . . , pn)-dominated multilinear operators and dominated (p1, . . . , pn;σ)-continuous multilinear operators. [ABSTRACT FROM PUBLISHER]

Copyright of El Profesional de la Información is the property of EPI SCP and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The (2-year) Impact Factor of Thomson-Reuters (IF) has become the fundamental tool for analysing the scientific production of academic researchers in a lot of countries. In this article we show that this index and the ordering criterion obtained by using it are highly unstable in the case of mathematics, to the extent that sometimes no reliability can be assigned to its use. We explain the reasons of this behaviour by the specific properties of the mathematical journals and publications, attending mainly the point of view of the researchers in pure mathematics. Using the Journal Citation Report list of journals as a source of information, we analyse the stability in the position of the mathematical journals--the so-called rank-normalized impact factor--compared with journals in applied physics and microbiology during the period 2002-12. Due to the lack of stability of the position of the journals of mathematics in these lists, we propose a 'cumulative index' that fits better the characteristics of mathematical journals. The computation of this index uses the values of the IF of the journals in previous years, providing in this way a more stable indicator. [ABSTRACT FROM AUTHOR]

In this note, we study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex set with non empty interior in (ℝ2,q), where q is an asymmetric lattice norm. [ABSTRACT FROM AUTHOR]

In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise products of Banach function spaces, spaces of integrable functions with respect to vector measures, spaces of operators, multipliers on Banach spaces of analytic functions and spaces of Lipschitz functions. [ABSTRACT FROM AUTHOR]

In this paper, we characterize compact linear operators from Banach function spaces to Banach spaces by means of approximations with bounded homogeneous maps. To do so, we undertake a detailed study of such maps, proving a factorization theorem and paying special attention to the equivalent strong domination property involved. Some applications to compact maximal extensions of operators are also given. [ABSTRACT FROM AUTHOR]

We study the Köthe dual spaces of Banach function lattices generated by abstract methods having roots in the theory of interpolation spaces. We apply these results to Banach spaces of integrable functions with respect to Banach space valued countably additive vector measures. As an application we derive a description of the Banach dual of a large class of these spaces, including Orlicz spaces of integrable functions with respect to vector measures. [ABSTRACT FROM AUTHOR]

Copyright of Anuario Think EPI is the property of EPI SCP and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

natural extension of the Daugavet property for p-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no reflexive space falls into this class. [ABSTRACT FROM AUTHOR]

Let (Ω, Σ) be a measurable space and m: Σ → X and m: Σ → X be positive vector measures with values in the Banach Köthe function spaces X and X. If 0 < α < 1, we define a new vector measure [ m, m] with values in the Calderón lattice interpolation space X X and we analyze the space of integrable functions with respect to measure [ m, m] in order to prove suitable extensions of the classical Stein-Weiss formulas that hold for the complex interpolation of L-spaces. Since each p-convex order continuous Köthe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces. [ABSTRACT FROM AUTHOR]

Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L 1( m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1( n) = L 1( m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L 1( m) associated to downward directed subsets of the set of all the representations. [ABSTRACT FROM AUTHOR]

A new stochastic approach for the approximation of (nonlinear) Lipschitz operators in normed spaces by their eigenvectors is shown. Different ways of providing integral representations for these approximations are proposed, depending on the properties of the operators themselves whether they are locally constant, (almost) linear, or convex. We use the recently introduced notion of eigenmeasure and focus attention on procedures for extending a function for which the eigenvectors are known, to the whole space. We provide information on natural error bounds, thus giving some tools to measure to what extent the map can be considered diagonal with few errors. In particular, we show an approximate spectral theorem for Lipschitz operators that verify certain convexity properties. [ABSTRACT FROM AUTHOR]

A phenomenological model that simulates the acoustic attenuation behavior of sonic crystals is developed in this paper. The input of the model is a set of parameters that characterizes each experimental setup, and the output is a simulation of the associated attenuation spectrum. The model consists of a combination of a multiresolution analysis based on wavelet functions and a set of artificial neural networks. An optimized coupling of these tools allows us to drastically reduce the experimental data needed, and to obtain a fast computational model that can be used for technological purposes. [ABSTRACT FROM AUTHOR]

Including designer preferences in every phase of the resolution of a multi-objective optimization problem is a fundamental issue to achieve a good quality in the final solution. To consider preferences, the proposal of this paper is based on the definition of what we call a preference basis that shows the preferred optimization directions in the objective space. Associated to this preference basis a new basis in the objective space—dominance basis—is computed. With this new basis the meaning of dominance is reinterpreted to include the designer's preferences. In this paper, we show the effect of changing the geometric properties of the underlying structure of the Euclidean objective space by including preferences. This way of incorporating preferences is very simple and can be used in two ways: by redefining the optimization problem and/or in the decision-making phase. The approach can be used with any multi-objective optimization algorithm. An advantage of including preferences in the optimization process is that the solutions obtained are focused on the region of interest to the designer and the number of solutions is reduced, which facilitates the interpretation and analysis of the results. The article shows an example of the use of the preference basis and its associated dominance basis in the reformulation of the optimization problem, as well as in the decision-making phase. [ABSTRACT FROM AUTHOR]

We show a simple model of the dynamics of a viral process based, on the determination of the Kaplan-Meier curve P of the virus. Together with the function of the newly infected individuals I, this model allows us to predict the evolution of the resulting epidemic process in terms of the number E of the death patients plus individuals who have overcome the disease. Our model has as a starting point the representation of E as the convolution of I and P. It allows introducing information about latent patients—patients who have already been cured but are still potentially infectious, and re-infected individuals. We also provide three methods for the estimation of P using real data, all of them based on the minimization of the quadratic error: the exact solution using the associated Lagrangian function and Karush-Kuhn-Tucker conditions, a Monte Carlo computational scheme acting on the total set of local minima, and a genetic algorithm for the approximation of the global minima. Although the calculation of the exact solutions of all the linear systems provided by the use of the Lagrangian naturally gives the best optimization result, the huge number of such systems that appear when the time variable increases makes it necessary to use numerical methods. We have chosen the genetic algorithms. Indeed, we show that the results obtained in this way provide good solutions for the model. [ABSTRACT FROM AUTHOR]

Let (Ω , Σ , μ) be a finite measure space and consider a Banach function space Y (μ) . We say that a Banach space E is representable by Y (μ) if there is a continuous bijection I : Y (μ) → E . In this case, it is possible to define an order and, consequently, a lattice structure for E in such a way that we can identify it as a Banach function space, at least regarding some local properties. General and concrete applications are shown, including the study of the notion of the pth power of a Banach space, the characterization of spaces of operators that are isomorphic to Banach lattices of multiplication operators, and the representation of certain spaces of homogeneous polynomials on Banach spaces as operators acting in function spaces. [ABSTRACT FROM AUTHOR]