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In this article we consider the set of all positive semidefinite linear operators on a finite-dimensional complex Hilbert space equipped with the so-called logarithmic product. We describe the general form of all automorphisms of this structure which are continuous at 0. [ABSTRACT FROM AUTHOR]

In this paper we describe the structure of all bijective nonlinear maps on the space of all bounded self-adjoint operators acting on a complex separable Hilbert space of dimension at least 3 which preserve a measure of commutativity, namely, the norm of the commutator of operators. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we present the complete description of surjective isometries of the space of all probability distribution functions on with respect to the Lévy metric. [Copyright &y& Elsevier]

In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions. [ABSTRACT FROM AUTHOR]

Abstract: Let be a finite-dimensional complex Hilbert space. The aim of this paper is to prove that every transformation on the space of all density operators on which preserves the relative entropy is implemented by either a unitary or an antiunitary operator on . [Copyright &y& Elsevier]

In this paper we describe the structure of all bijective linear maps between the spaces of self-adjoint elements of von Neumann algebras that preserve the so-called maximal deviation. It turns out that those transformations are closely related to Jordan *-isomorphisms. [ABSTRACT FROM PUBLISHER]

Abstract: Let be a complex Hilbert space. The symbol stands for the harmonic mean of the positive bounded linear operators on in the sense of Ando. In this paper we describe the general form of all automorphisms of the set of positive operators with respect to that operation. We prove that any such transformation is implemented by an invertible bounded linear or conjugate-linear operator on . Similar results concerning the parallel sum and the arithmetic mean in the place of the harmonic mean are also presented. [Copyright &y& Elsevier]

Abstract: In this paper we describe the general forms of surjective isometries of the space of all probability distribution functions on with respect to the Kolmogorov–Smirnov metric. [Copyright &y& Elsevier]

Abstract: We define a natural metric on the space of all bounded frame functions on a given Hilbert space and also on the space of all bounded frame functions with a given weight. We present the complete description of the surjective isometries of the so-obtained metric spaces. In fact, it turns out that those isometries are intrinsically induced by unitary or antiunitary operators on the underlying Hilbert space. [Copyright &y& Elsevier]

We describe the general form of bijective maps on the space of all Hilbert space effects or all observables on a finite dimensional space which preserve the spectral order in both directions. [ABSTRACT FROM AUTHOR]

Abstract: Let H be a Hilbert space and let and be standard ∗-operator algebras on H. Denote by and the set of all self-adjoint operators in and , respectively. Assume that and are surjective maps such that and for every pair , . Then there exist an invertible bounded linear or conjugate-linear operator and a constant such that , , and , . [Copyright &y& Elsevier]

In this article after defining the abstract concept of compatibility-like functions on quantum states, we prove that every bijective transformation on the set of all states which preserves such a function is implemented by an either unitary or antiunitary operator. [ABSTRACT FROM AUTHOR]

Let H be a separable infinite-dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on H without the assumption on continuity are also presented. [ABSTRACT FROM AUTHOR]

The set of all effects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set. [ABSTRACT FROM AUTHOR]

Let H be a separable infinite-dimensional complex Hilbert space. We prove that if Ф: ℬ( H)→ℬ( H) is a-preserving ring homomorphism whose range contains a rank-one operator and an operator with dense range, then Ф is an isometric linear or conjugate-linear algebra automorphism of ℬ( H). In particular, if the unilateral shift is contained in the range of a-endomorphism Ф of ℬ( H), then Ф is bijective. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the authors discuss various reports within the issue including topics on mathematical structure, models, and mechanics.

In this paper we consider three operations on positive definite cones of C ⁎ -algebras which are related to weighted geometric means and appear in the formulas defining various versions of quantum Rényi relative entropy. We show how Jordan *-isomorphisms between C ⁎ -algebras can be characterized by the preservation of the norms of products under those operations or by the preservation of the operations themselves. We also obtain conditions for the commutativity of the underlying algebras by showing that we have that property if one of the quantities under considerations can be transformed by a surjective map to another different such quantity. [ABSTRACT FROM AUTHOR]

An excerpt from the book "Athletika," by Lajos Molnár is presented.

Abstract: We establish the algebraic reflexivity of three isometry groups of operator structures: the group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of , the operator algebra over a complex infinite dimensional separable Hilbert space . We show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the reflexivity of some automorphism groups. [Copyright &y& Elsevier]

Since it is Hungary's second largest river, the River Tisza is important both as a river and because of its active floodplain. The contaminations endanger the aquatic and the related living nature as well as the farming in the active floodplain. The water quality of the river is examined regularly by the competent authority but far less information is available about the active floodplain. More data is necessary in order to estimate the potential danger. In this paper the River Tisza and its tributaries were examined, especially considering the metal accumulation and its relation to the soil characteristics. We started to create the database in 2004 and several tasks were achieved: the metal content of the root zone in the active floodplain (horizontal distribution); the metal content of the upper 1 m zone in the active floodplain (vertical distribution); the general water chemical and isotope analyses and the metal content of the oxbow lakes near the River Tisza; the metal content of the sediments of the oxbow lakes. More than 300 surface soil samples, 18 soil profiles (18 x 50 samples) and 45 oxbow lakes were examined up to now. Cu, Co, Fe, Ni, Mn, Zn contents were determined in every case and As, Cd, Pb determinations were also carried out in reasonable cases. ArcGIS 9.0 was applied in order to create the spatial database and the statistical analyses of the data were carried out with SPSS. In this paper some case studies will be presented. [ABSTRACT FROM AUTHOR]