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A study of the class \Delta consisting of topological \Delta-spaces was originated by Jerzy Ka̧kol and Arkady Leiderman [Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 86–99; Proc. Amer. Math. Soc. Ser. B 8 (2021), pp. 267–280]. The main purpose of this paper is to introduce and investigate new classes \Delta _2 \subset \Delta _1 properly containing \Delta. We observe that for every first-countable X the following equivalences hold: X\in \Delta _1 iff X\in \Delta _2 iff each countable subset of X is G_{\delta }. Thus, new proposed concepts provide a natural extension of the family of all \lambda-sets beyond the separable metrizable spaces. We prove that (1) A pseudocompact space X belongs to the class \Delta _1 iff countable subsets of X are scattered. (2) Every regular scattered space belongs to the class \Delta _2. We investigate whether the classes \Delta _1 and \Delta _2 are invariant under the basic topological operations. Similarly to \Delta, both classes \Delta _1 and \Delta _2 are invariant under the operation of taking countable unions of closed subspaces. In contrast to \Delta, they are not preserved by closed continuous images. Let Y be l-dominated by X, i.e. C_p(X) admits a continuous linear map onto C_p(Y). We show that Y \in \Delta _1 whenever X \in \Delta _1. Moreover, we establish that if Y is l-dominated by a compact scattered space X, then Y is a pseudocompact space such that its Stone–Čech compactification \beta Y is scattered. [ABSTRACT FROM AUTHOR]

In this paper, we consider all possible variants of Choi matrices of linear maps, and show that they are determined by non-degenerate bilinear forms on the domain space. We will do this in the setting of finite dimensional vector spaces. In case of matrix algebras, we characterize all variants of Choi matrices which retain the usual correspondences between k-superpositivity and Schmidt number ≤ k as well as k-positivity and k-block-positivity. We also compare de Pillis' definition [Pac. J. Math. 23, 129–137 (1967)] and Choi's definition [Linear Algebra Appl. 10, 285–290 (1975)], which arise from different bilinear forms. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

Linear operators with off‐diagonal decay appear in many areas of mathematics including harmonic and numerical analysis, and their stability is one of the basic assumptions. In this paper, we consider a family of localized integral operators in the Beurling algebra with kernels having mild singularity near the diagonal and certain Hölder continuity property, and prove that their weighted stabilities for different exponents and Muckenhoupt weights are equivalent to each other on a space of homogeneous type with Ahlfors regular measure. [ABSTRACT FROM AUTHOR]

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation theorem concerning the fuzzy rate of convergence of these operators. Furthermore, through an example, we illustrate that our summability- based Korovin type theorem has an advantage over the fuzzy Korovkin type theorem proved in the seminal paper by Anastassiou (Stud. Univ. Babeş-Bolyai Math L(4):3–10, 2005) [ABSTRACT FROM AUTHOR]

Given two square matrices A, B of the same size, the two matrices AB and BA may have different ranks. A non-zero square matrix A is called a rankcommutator of a family L of n × n matrices if rank(AL) = rank(LA) holds for every L in L. Let L* denote the family of all rank-commutators of L. In this paper, we investigate the members of L* for the following families L of n×n matrices: all non-zero symmetric matrices; all diagonal matrices; all diagonalizable matrices. In the process, some new notions in linear algebra are created, such as "rank-symmetric matrices" and "determinant equivalent matrices", which might be useful for other study on ranks. A few problems for further study are posed at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar. [ABSTRACT FROM AUTHOR]

Let A be an Archimedean f-algebra, let x ∈ A , and let π x : A → A be the linear map defined by π x y = x y , for all y ∈ A. The aim of our paper is to give necessary and sufficient conditions concerning the averaging property of (r.u) continuous projections on Archimedean f-algebras, with a range, R T , a vector sublattice of A, that maps weak order units into weak order units. As an application, we prove that if A is an Archimedean f-algebra with a unit element e, T is a positive projection on A, with a range, R T , a vector sublattice of A, such that T(e) is a weak order unit of A, then T is an averaging operator if and only if R T is π T e - invariant subspace. This improves considerably a result of Kuo et al. (J Math Anal Appl 303:509–521, 2005). [ABSTRACT FROM AUTHOR]

This paper deals with a conjecture posed by Abbas Salemi in 2011 (Banach J. Math. Anal.), claiming that for the spectrum of every bounded linear operator on a separable Hilbert space there exists an estimable total decomposition. We partially solve this problem, in the sense that, for the normal operator, there exists an estimable decomposition, under approximately unitary equivalence. [ABSTRACT FROM AUTHOR]

In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented. [ABSTRACT FROM AUTHOR]

The integral operator Lmp (λ, ℓ)(λ, ℓ > 0; p ∈ N; m ∈ N0 = N ∪ {0}, where N = {1, 2, ...}) for functions of the form f(z) = z-p + P∞k=p+1 akzk which are analytic and p-valent in the punctured open unit disc U∗ = {z ∈ C : 0 < |z| < 1} = U\{0} was introduced by El-Ashwah [7]. The objective of the present paper is to extend the definition of the operator Lmp (λ, ℓ)f(z) for m ∈ Z = {0, ±1, ±2, ...} and drive interesting argument results of p-valent meromorphic functions defined by this differintegral operator. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of unitary operators defined on the Bergman space L²a (C+) of the right half plane C+ and study certain algebraic properties of these operators. Using these results, we then show that a bounded linear operator S from L²a(C+) into itself commutes with all the weighted composition operators Wa,a £ D if and only if S(w) = {Sbw,bw),w £ C+ satisfies a certain averaging condition. Here for a = c + id £ D, f £ L2a(C+),Waf = ... Some applications of these results are also discussed. [ABSTRACT FROM AUTHOR]

In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable F-spaces. It is proven that a linear operator T on topological vector space X is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on c0(Z) and c0(N), respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators λI +μB, where I is identity and B is backward shift. We note that there are essential differences between the non-Archimedean and real cases. [ABSTRACT FROM AUTHOR]

Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned. [ABSTRACT FROM AUTHOR]

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks. Moreover, there has been no rate of convergence analysis for the ADMM without strong convexity in the objective function. In this paper we establish the global R-linear convergence of the ADMM for minimizing the sum of any number of convex separable functions, assuming that a certain error bound condition holds true and the dual stepsize is sufficiently small. Such an error bound condition is satisfied for example when the feasible set is a compact polyhedron and the objective function consists of a smooth strictly convex function composed with a linear mapping, and a nonsmooth $$\ell _1$$ regularizer. This result implies the linear convergence of the ADMM for contemporary applications such as LASSO without assuming strong convexity of the objective function. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the study of the diamond partial order in C * -algebras. We characterize linear maps preserving this partial order. [ABSTRACT FROM AUTHOR]

In this paper we present some new operator inequality for convex functions. We have obtained a number of Jensen's type inequalities for convex and operator convex functions of self-adjoint operators for positive linear maps. Some results are exemplified for power and logarithmic functions. [ABSTRACT FROM AUTHOR]

The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e 0 (x) = 1 and e 1 (x) = x , e 0 (x) = 1 and e 2 (x) = x 2 , as well as e 1 (x) = x and e 2 (x) = x 2 . The class of operators that preserve the test functions e 1 (x) = x and e 2 (x) = x 2 is a genuine generalization of the class introduced by Indrea et al. in their paper "A New Class of Kantorovich-Type Operators", published in Constr. Math. Anal. [ABSTRACT FROM AUTHOR]

For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operator $${U_{k,\phi}^{\beta}}$$ on $${L^{2}(\beta)}$$ with $${\phi \in L^{\infty}(\beta)}$$ is defined as $${U_{k,\phi}^{\beta}=W_{k}M_{\phi}^{\beta}}$$ , where $${W_{k}e_{n}(z)=\frac{\beta_{m}}{\beta_{km}}e_m(z)}$$ if $${n=km, m\in\mathbb{Z}}$$ and $${W_{k}e_n(z)= 0}$$ if n ≠ km. The paper derives relations among the symbols of two kth-order slant weighted Toeplitz operators so that their product is a kth-order slant weighted Toeplitz operator. We also discuss the compactness and the case for two kth-order slant weighted Toeplitz operators to commute essentially. [ABSTRACT FROM AUTHOR]

In this paper, we study existence of isometric embedding of S q m into S p n , where 1 ≤ p ≠ q ≤ ∞ and n ≥ m ≥ 2. We show that for all n ≥ m ≥ 2 if there exists a linear isometry from S q m into S p n , where (q , p) ∈ (1 , ∞ ] × (1 , ∞) ∪ (1 , ∞) ∖ { 3 } × { 1 , ∞ } and p ≠ q , then we must have q = 2. This mostly generalizes a classical result of Lyubich and Vaserstein. We also show that whenever S q embeds isometrically into S p for (q , p) ∈ (1 , ∞) × [ 2 , ∞) ∪ [ 4 , ∞) × { 1 } ∪ { ∞ } × (1 , ∞) ∪ [ 2 , ∞) × { ∞ } with p ≠ q , we must have q = 2. Thus, our work complements work of Junge, Parcet, Xu and others on isometric and almost isometric embedding theory on non-commutative L p -spaces. Our methods rely on several new ingredients related to perturbation theory of linear operators, namely Kato-Rellich theorem, theory of multiple operator integrals and Birkhoff-James orthogonality, followed by thorough and careful case by case analysis. The question whether for m ≥ 2 and 1 < q < 2 , S q m embeds isometrically into S ∞ n , was left open in Bull. London Math. Soc. 52 (2020) 437-447. [ABSTRACT FROM AUTHOR]

In this paper, we present some new reverse arithmetic–geometric mean inequalities for operators and matrices due to Lin (Stud. Math. 215:187–194, 2013). Among other inequalities, we prove that if A , B ∈ B (H) are accretive and 0 < m I ≤ ℜ (A) , ℜ (B) ≤ M I , then, for every positive unital linear map Φ, Φ 2 (ℜ (A + B 2)) ≤ (K (h)) 2 Φ 2 (ℜ (A ♯ B)) , where K (h) = (h + 1) 2 4 h and h = M m . Moreover, some reverse harmonic–geometric mean inequalities are also presented. [ABSTRACT FROM AUTHOR]

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the powered Baskakov basis. We prove that in the particular case of squared Baskakov basis the operators behave better than the classical Baskakov operators. For this particular case we give also a quantitative Voronovskaya type result. [ABSTRACT FROM AUTHOR]