Linear Algebra and its Applications, ( ISI ), Volume (439), No (3), Year (2013-6) , Pages (584-591)

#### Title : ( An operator inequality and its consequences )

Citation: BibTeX | EndNote

#### Abstract

Let $f$ be a continuous convex function on an interval $J$, let $A, B, C, D$ be self-adjoint operators acting on a Hilbert space with spectra contained in $J$ such that $A+D=B+C$ and $A\\\\leq m\\\\leq B,C\\\\leq M \\\\leq D$ for two real numbers $m<M$, and let $\\\\Phi$ be a unital positive linear map on $\\\\mathbb{B}(\\\\mathscr{H})$. We prove the inequality \\\\begin{eqnarray*} f(\\\\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.

#### Keywords

, Operator inequality, convex function, positive linear map, Jensen--Mercer operator inequality, Petrovi\\\\\\\'c operator inequality
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@article{paperid:1029100,
title = {An operator inequality and its consequences},
journal = {Linear Algebra and its Applications},
year = {2013},
volume = {439},
number = {3},
month = {June},
issn = {0024-3795},
pages = {584--591},
numpages = {7},
keywords = {Operator inequality; convex function; positive linear map; Jensen--Mercer operator inequality; Petrovi\\\\\\\'c operator inequality},
}