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 $ ...

|.

\\end{eqnarray*}

This inequality was studied and extended by a number of mathematicians for different contents such as inner product spaces,

quadrature formulae, finite Fourier transforms and linear functionals.



For unital $n$-positive linear maps $\\Phi$ ($n...

‎Let $C$ and $D$ be positive operators such that $C\\leq D$ and $D$ be invertible‎. ‎We show that there exists a trace preserving unital completely positive map $\\Phi_{C,D}:\\mathbb{B}(\\mathcal{H})\\rightarrow ...

In this paper, we give some Gr¨uss type inequalities for the trace on a noncommutative probability space (A, τ ). In fact, we generalize a Gr¨uss type inequality, which extends a result obtained by P. F. Renaud.

We introduce and investigate the notion of an operator P-class function. We show that every nonnegative operator convex function is of operator P-class, but the converse is not true in general. We present some Jensen type ...

We study the operator $Q$-class functions, present some Hermite--Hadamard inequalities for operator $Q$-class functions and give some Kantorovich and Jensen type operator inequalities involving $Q$-class functions.

, then for every unital positive linear map Φ the following inequalities hold:

View the MathML source(Φ(A)♯Φ(B))2≤(M1M2+m1m22M1M2m1m2)4Φ(A♯B)2

Turn MathJax on and View the MathML source...

We investigate positive definite solutions of nonlinear matrix equations $X-f(\\Phi(X))=Q$ and $X-\\sum_{i=1}^{m}f(\\Phi_i(X))=Q$, where $Q$ is a positive definite matrix, $\\Phi$ and $\\Phi_i ~~(1\\leq i\\leq m)$ are positive linear maps...

We extend an operator P\\'{o}lya--Szeg\\"{o} type inequality involving the operator geometric mean to any arbitrary operator mean under some mild conditions. Utilizing the Mond--Pe\\v{c}ari\\'c method, we present some other ...

{A} \\longrightarrow \\mathcal{B}$ is a unital positive linear map, then

\\begin{eqnarray*}

\\big|\\Phi(AB)-\\Phi(A)\\Phi(B)\\big| \\leq \\big\\|\\Phi(|A^*-\\zeta I|^2)\\big\\|^\\frac{1}{2} \\big[\\Phi(|B-\\xi I|^2)\\big]^\\frac{1}{2}...