Let $A, B$ be positive definite $n\\times n$ matrices. We present several reverse Heinz type inequalities, in particular \\begin{align*} \\|AX+XB\\|_2^2+ 2(\\nu-1) \\|AX-XB\\|_2^2\\leq \\|A^{\\nu}XB^{1-\\nu}+A^{1-\\nu}XB ...

In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove that for all $0\\leq \\nu\\leq 1$ and ...

Let $A$ and $B$ be two positive operators with $0 < m \\leqslant

A, B \\leqslant M$ for positive real numbers $ M, m, \\, \\sigma$

be an operator mean and $\\sigma^{*}$ be the adjoint

mean of $ \\sigma.$ If $\\sigma...

‎The aim of this paper is to find some sufficient conditions for positivity of block matrices of positive operators‎.

‎It is shown that for positive operators $A,B,C$ and for every non-negative operator monotone ...

We present a Bellman inequality involving operator means for

operators acting on a Hilbert space. We also give some Bellman

inequalities concerning sesquilinear forms. Finally, we refine the

Jensen's operator inequality and use...

We establish several operator extensions of the Chebyshev inequality. The main version deals with the Hadamard product of Hilbert space operators. More precisely, we prove that if $\\mathscr{A}$ is a $C^*$-algebra, $T$ is ...

_j\\right)\\sharp \\left(\\sum_{ j=1}^nB_j\\right)\\,,

\\end{align*}

where $A_j, B_j\\,\\,(1\\leq j\\leq n)$ are positive invertible operators and $\\sigma$ and $\\sigma^\\perp$ are an operator mean and its dual in the sense of Kabo and Ando, respectively...

that the obtained class represents the weighted logarithmic means. We shall also consider weighted identric mean and some relationships between various operator means. Among many things, we extended the weighted arithmetic--geometric operator mean inequality as $A...

We present an operator version of the Callebaut inequality

involving the interpolation paths and apply it to the weighted

operator geometric means. We also establish a matrix version of the

Callebaut ...

We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\\in {\\mathfrak B...