(\\\\\\\\Phi(B))+f(\\\\\\\\Phi(C))\\\\\\\\leq \\\\\\\\Phi(f(A))+\\\\\\\\Phi(f(D)).

\\\\\\\\end{eqnarray*}

and apply it to obtain several inequalities such as the

Jensen--Mercer operator inequality and the Petrovi\\\\\\\\\\\\\\'c operator

inequality....

‎Let BJ(H) denote the set of self-adjoint operators acting on a Hilbert space H with spectra contained in an open interval J. A map Φ:BJ(H)→B(H)sa is said to be of Jensen-type if (C∗AC+D∗BD)≤C∗Φ(A)C+D∗Φ(B)D for all ...

While Professor J.E. Peˇcari´c and the interviewer are meeting each

other in three conferences in Iran, Hungary and Croatia, they had some conversations

concerning life, ideas and contributions of Professor ...

We present some generalized Jensen type operator inequalities

involving sequences of self-adjoint operators. Among other things,

we prove that if f:[0, infty) to mathbb{R} is a continuous

convex function with f(0) leq 0...

on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert $C^*$-modules. In particular, we pay special attention to an operator Wielandt inequality....

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 $ ...

We present an operator version of the Karamata inequality. More

precisely, we prove that if $A$ is a selfadjoint element of a unital

C^* -algebra mathscr{A} , rho is a state on mathscr{A} , the

functions ...

Using a $2\\\\\\\\\\\\\\\\times 2$ matrix trick, we present an inequality

involving commutators of certain Hilbert space operators as an

operator version of Buzano\\\\\\\\\\\\\\'s inequality, which is in turn ...

This paper focuses on Riemann sums for the functional calculus of bounded self-adjoint operaors. We first obtain some monotonicity properties of operator convex functions. Using these results we then refine an

operator ...

Assuming a unitarily invariant norm $...
|\\cdot...
|$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $...
|\\cdot...
|$ on matrix algebras $\\mathcal{M}_n$ for all finite values of $n$ via $...
|A...
|=...
|A\\oplus 0...
|$. We show that if $\\mathscr{A}$ is a $C^*$-algebra of finite dimension

$k$ and $\\Phi: \\mathscr{A} \\to \\mathcal{M}_n$ is a unital completely

positive map, then

\\begin{equation*}

...
|\\Phi(AB)-\\Phi(A)\\Phi(B)...
| \\leq \\frac{1}{4}

...
|I_{n}...
|\\,...
|I_{kn}...
{M}_{m}$. Further we get an analogous

inequality for certain $n$-positive maps in the setting of full

matrix algebras by using some matrix tricks. We also give a Gr\\"uss

operator inequality in the setting of $C^*$-algebras of arbitrary...