Related papers: On characterization of operator monotone functions
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
In a recent paper (2024) Camacho, C\'{a}novas, Mart\'{\i}nez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility…
We investigate the operator monotonicity of functions which was considered by V.E. Szabo.
Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of "identifiability", a common property of…
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference…
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…
It is a classical result in complex analysis that the class of functions that arise as the Cauchy transform of probability measures may be characterized entirely in terms of their analytic and asymptotic properties. Such transforms are a…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite-Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for…
We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigroups in Banach spaces with Fourier type.
A. Tarski proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and…
This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
Matrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for matrix-valued Cauchy bi-orthogonal polynomials…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical…
We study in this article a new pointwise estimate for ''rough'' singular integral operators. From this pointwise estimate we will derive Sobolev type inequalities in a variety of functional spaces.
In this paper, we introduce and study a new classes of operators, named AM-unbounded norm compact operators. We study the the basic properties of the new operator and we investigate the lattice-order and topology property of the operator…
A new type of combinations of Bernstein operators is given in [1]. Here, we introduce another one, which can be used to approximate the functions with singularities. The direct and inverse results of the weighted approximation of this new…