Related papers: Jensen's operator inequality and its converses

Employing the notion of operator log-convexity, we study joint concavity$/$ convexity of multivariable operator functions: $(A,B)\mapsto F(A,B)=h\left[ \Phi(f(A))\ \sigma\ \Psi(g(B))\right]$, where $\Phi$ and $\Psi$ are positive linear maps…

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…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

In this paper we introduce operator s-convex func- tions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

The main aim of this book is to present recent results concerning inequalities for continuous functions of selfadjoint operators on complex Hilbert spaces. It is intended for use by both researchers in various fields of Linear Operator…

In this paper, we improve the famous Reid Inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid and…

In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of $v$, namely $v\in \mathbb{R}$. These modified inequalities are used to establish corresponding operator inequalities on a…

In this short note, we improve the famous Reid Inequality related to linear operators.

In this paper necessary conditions and sufficient conditions are given for a linear operator to be a positive operators of an Extended Lorentz cone. Similarities and differences with the positive operators of Lorentz cones are investigated.

For a positive and invertible linear operator $T$ acting on a $C^*$-algebra, we give necessary and sufficient criteria for the inverse operator $T^{-1}$ to be positive, too. Moreover, a simple counterexample shows that $T^{-1}$ need not be…

The purpose of this paper is to establish the weighted norm inequalities of one-sided oscillatory integral operators by the aid of interpolation of operators with change of measures.

The main purpose of this paper is to establish some isoperimetric type inequalities for mappings induced by the weighted Laplace differential operators. The obtained results of this paper provide improvements and extensions of the…

We give an extension of Hua's inequality in pre-Hilbert $C^*$-modules without using convexity or the classical Hua's inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen…

Some new inequalities for the norm and the numerical radius of composite operators generated by a pair of operators are given.

We prove inequalities on symmetric tensor sums of positive definite operators. In particular, we prove multivariable operator inequalities inspired by generalizations to the well-known Hlawka and Popoviciu inequalities. As corollaries, we…

The purpose of this paper is to present some general inequalities for operator concave functions which include some known inequalities as a particular case. Among other things, we prove that if $A\in \mathcal{B}\left( \mathcal{H} \right)$…

The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…

Theorem 1. Given a number c >= 1, there exists a J-unitary operator \hat{V}, such that: (a) r(\hat{V})= r(\hat{V}^{-1})= c ; (b) S(c^{-1}\hat{V})=S(c^{-1}\hat{V}^{-1}) =S(c^{-1}\hat{V}^{*-1}) = S(c^{-1}\hat{V}^*)={0} (c) there exist maximal…

We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our…