Related papers: Ando-Hiai type inequalities for multivariate opera…
By means of a fixed point method we discuss the deformation of operator means and multivariate means of positive definite matrices/operators. It is shown that the deformation of an operator mean becomes again an operator mean. The means…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
In this paper, we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some compact generalizations of the well-known inequalities of Bernstein,…
We improve the operator Kantorovich inequality as follows: Let $A$ be a positive operator on a Hilbert space with $0<m\le A \le M$. Then for every unital positive linear map $\Phi$, \[\Phi(A^{-1})^2\le (\frac{(M+m)^2}{4Mm})^2\Phi(A)^{-2}.\]…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
In this paper we present some characterizations for quasi-arithmetic operator means (among them the arithmetic and harmonic means) on the positive definite cone of the full algebra of Hilbert space operators, and also for the Kubo-Ando…
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
We consider the Grushin type operator on $\mathbb{R}^{d}_x \times \mathbb{R}^{k}_y$ with the form \begin{equation*}…
Recently, the spectral geometric mean has been studied by some papers. In this paper, we firstly estimate the H\"{o}lder type inequality of the spectral geometric mean of positive invertible operators on the Hilbert space for all real order…
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary…
Through a new powerful potential-theoretic analysis, this paper is devoted to discovering the geometrically equivalent isocapacity forms of Chou-Wang's Sobolev type inequality and Tian-Wang's Moser-Trudinger type inequality for the fully…
In this work, generalization of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of selfadjoint linear operators in Hilbert spaces are proved.
We consider the Harnack inequality for harmonic functions with respect to three types of infinite dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack…
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some…
We prove here the Melin H\"ormander inequality for operators with multiple characteristics.
We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present converse of Ando's inequality, for each parameter. We give examples to compare our results with the known…
In this paper we first introduce the Heron and Heinz means of two convex functionals. Afterwards, some inequalities involving these functional means are investigated. The operator versions of our theoretical functional results are…