Title : ( An operator Karamata inequality )
Authors: Mohammad Sal Moslehian , Marek Niezgoda , Rajna Rajic ,
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Abstract
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 f, g$ are continuous on the spectrum sigma(A) of A such that 0<m_1 le f(s) le M_1 , 0<m_2 le g(s) le M_2 for all s in sigma(A) and K= left( sqrt{m_1m_2}+ sqrt{M_1M_2} right)/ left( sqrt{m_1M_2}+ sqrt{M_1m_2}right) , then K^{-2} le frac{ rho(f(A)g(A))}{ rho(f(A)) rho(g(A))} le K^2. We also give some applications.
Keywords
, Karamata inequality, operator inequality, positive operator, C*-algebra
@article{paperid:1036577,
author = {Sal Moslehian, Mohammad and Marek Niezgoda and Rajna Rajic},
title = {An operator Karamata inequality},
journal = {Bulletin of the Malaysian Mathematical Sciences Society},
year = {2014},
volume = {37},
number = {4},
month = {June},
issn = {0126-6705},
pages = {949--954},
numpages = {5},
keywords = {Karamata inequality; operator inequality; positive operator; C*-algebra},
}
%0 Journal Article
%T An operator Karamata inequality
%A Sal Moslehian, Mohammad
%A Marek Niezgoda
%A Rajna Rajic
%J Bulletin of the Malaysian Mathematical Sciences Society
%@ 0126-6705
%D 2014
