Positivity, ( ISI ), Volume (22), No (5), Year (2018-10) , Pages (1255-1263)

Title : ( Operator maps of Jensen-type )

Authors: , Mohammad Sal Moslehian , Hamed Najafi ,

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Abstract

‎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 A,B∈BJ(H) and bounded linear operators C, D acting on H with C∗C+D∗D=I, where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form Φ(A)=f(A) for some operator convex function f defined in J.

Keywords

, ensen’s operator inequality, Convex operator function
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@article{paperid:1067784,
author = { and Sal Moslehian, Mohammad and Najafi, Hamed},
title = {Operator maps of Jensen-type},
journal = {Positivity},
year = {2018},
volume = {22},
number = {5},
month = {October},
issn = {1385-1292},
pages = {1255--1263},
numpages = {8},
keywords = {ensen’s operator inequality; Convex operator function},
}

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%0 Journal Article
%T Operator maps of Jensen-type
%A
%A Sal Moslehian, Mohammad
%A Najafi, Hamed
%J Positivity
%@ 1385-1292
%D 2018

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