Linear and Multilinear Algebra, ( ISI ), Volume (70), No (17), Year (2020-10) , Pages (3287-3300)

Title : ( Asymmetric Choi–Davis inequalities )

Authors: Mohsen Kian , Mohammad Sal Moslehian , R. Nakamoto ,

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‎Let $\\\\\\\\\\\\\\\\Phi$ be a unital positive linear map and let $A$ be a positive invertible operator‎. ‎We prove that there exist partial isometries $U$ and $V$ such that‎ ‎\\\\\\\\\\\\\\\\[ |\\\\\\\\\\\\\\\\Phi(f(A))\\\\\\\\\\\\\\\\Phi(A)\\\\\\\\\\\\\\\\Phi(g(A))|\\\\\\\\\\\\\\\\leq U^*\\\\\\\\\\\\\\\\Phi(f(A)Ag(A))U‎ ‎\\\\\\\\\\\\\\\\]‎ ‎and‎ ‎\\\\\\\\\\\\\\\\[\\\\\\\\\\\\\\\\left|\\\\\\\\\\\\\\\\Phi\\\\\\\\\\\\\\\\left(f(A)\\\\\\\\\\\\\\\\right)^{-r}\\\\\\\\\\\\\\\\Phi(A)^r\\\\\\\\\\\\\\\\Phi\\\\\\\\\\\\\\\\left(g(A)\\\\\\\\\\\\\\\\right)^{-r}\\\\\\\\\\\\\\\\right|\\\\\\\\\\\\\\\\leq V^*\\\\\\\\\\\\\\\\Phi\\\\\\\\\\\\\\\\left(f(A)^{-r}A^rg(A)^{-r}\\\\\\\\\\\\\\\\right)V\\\\\\\\\\\\\\\\]‎ ‎hold under some mild operator convex conditions and some positive numbers $r$‎. ‎Further‎, ‎we show that if $f^2$ is operator concave‎, ‎then‎ ‎$$ |\\\\\\\\\\\\\\\\Phi(f(A))\\\\\\\\\\\\\\\\Phi(A)|\\\\\\\\\\\\\\\\leq \\\\\\\\\\\\\\\\Phi(Af(A)).$$‎ ‎In addition‎, ‎we give some counterparts to the asymmetric Choi--Davis inequality and asymmetric Kadison inequality‎. ‎Our results extend some inequalities due to Bourin--Ricard and Furuta‎.


, Choi--Davis inequality‎, ‎positive linear map‎, ‎Kadison inequality‎, ‎Kantorovich constant
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author = {Mohsen Kian and Sal Moslehian, Mohammad and R. Nakamoto},
title = {Asymmetric Choi–Davis inequalities},
journal = {Linear and Multilinear Algebra},
year = {2020},
volume = {70},
number = {17},
month = {October},
issn = {0308-1087},
pages = {3287--3300},
numpages = {13},
keywords = {Choi--Davis inequality‎; ‎positive linear map‎; ‎Kadison inequality‎; ‎Kantorovich constant},


%0 Journal Article
%T Asymmetric Choi–Davis inequalities
%A Mohsen Kian
%A Sal Moslehian, Mohammad
%A R. Nakamoto
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2020