Related papers: On characterization of operator monotone functions
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
In this paper, we consider the structure of maximally monotone operators in Banach space whose domains have nonempty interior and we present new and explicit structure formulas for such operators. Along the way, we provide new proofs of the…
In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these results, we present some functional inequalities (like Tur\'an…
Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…
We prove that there is a bijection between the families of regular and non-regular operator monotone functions. As an application we give a new proof of the operator monotonicity of a certain class of functions related to…
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…
We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…
Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators.…
In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.
In this paper our aim is to prove some monotonicity and convexity results for the modified Struve function of the second kind by using its integral representation. Moreover, as consequences of these results, we present some functional…
We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.
In this paper, we introduce the concept of operator arithmetic-geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities…
A new class of operators, larger than $C$-symmetric operators and different than normal one, named $C$--normal operators is introduced. Basic properties are given. Characterizations of this operators in finite dimensional spaces using a…
We study the relations between some geometric properties of maximal monotone operators and generic geometric and analytical properties of the functions on the associate Fitzpatrick family of convex representations. We also investigate under…
Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on…
The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…
We characterize matrix-valued asymmetric truncated Toeplitz operators (which are compressions of multiplication operators acting between two possibly different model spaces) by using compressed shifts, modified compressed shifts and shift…
Based on the concept of unbounded absolutely weakly convergence, we give new characterizations of L-weakly compact sets. As applications, we find some properties of order weakly compact operators. Also, a new characterizations of order…
In this paper, we survey recent progress on the theory of maximally monotone operators in general Banach space. We also extend various of the results and leave some open questions.
The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in $[0,+\infty]$ and to vanish only on the graph of the operator.…