Title : ( Refinements of Choi--Davis--Jensen s inequality )
Authors: J.S. Aujla , S.S. Dragomir , M. Khosravi , Mohammad Sal Moslehian ,
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Abstract
Let Phi_1, ldots, Phi_n be strictly positive linear maps from a unital C^* -algebra { mathscr A} into a C^* -algebra mathscr B and let Phi= sum_{i=1}^n Phi_i be unital. If f is an operator convex function on an interval J , then for every self-adjoint operator A in mathscr A with spectrum contained in J , the following refinement of the Choi--Davis--Jensen inequality holds: begin{eqnarray*} f( Phi(A)) leq sum_{i=1}^n Phi_i(I)^{ frac{1}{2}}f left( Phi_i(I)^{- frac{1}{2}} Phi_i(A) Phi_i(I)^{- frac{1}{2}} right) Phi_i(I)^{ frac{1}{2}} leq Phi(f(A)) ,.
Keywords
, Choi, , Davis, , Jensen s inequality; operator convex; operator inequality; Hilbert C^* , module; positive map
@article{paperid:1021828,
author = {J.S. Aujla and S.S. Dragomir and M. Khosravi and Sal Moslehian, Mohammad},
title = {Refinements of Choi--Davis--Jensen s inequality},
journal = {Bulletin of Mathematical Analysis and Applications},
year = {2011},
volume = {3},
number = {2},
month = {September},
issn = {1821-1291},
pages = {127--133},
numpages = {6},
keywords = {Choi--Davis--Jensen s inequality; operator convex;
operator inequality; Hilbert C^* -module; positive map},
}
%0 Journal Article
%T Refinements of Choi--Davis--Jensen s inequality
%A J.S. Aujla
%A S.S. Dragomir
%A M. Khosravi
%A Sal Moslehian, Mohammad
%J Bulletin of Mathematical Analysis and Applications
%@ 1821-1291
%D 2011
