Topological Algebra and its Applications, Volume (1), No (1), Year (2013-4) , Pages (9-21)

Title : ( Operator inequalities of Jensen type )

Authors: Mohammad Sal Moslehian , Jadranka Micic , Mohsen Kian ,

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We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f:[0, infty) to mathbb{R} is a continuous convex function with f(0) leq 0 , then begin{equation*} sum_{i=1}^{n} f(C_i) leq f left( sum_{i=1}^{n}C_i right)- delta_fsum_{i=1}^{n} widetilde{C}_i leq f left( sum_{i=1}^{n}C_i right) end{equation*} for all operators C_i such that 0 leq C_i leq M leq sum_{i=1}^{n} C_i (i=1, ldots,n) for some scalar M geq0 , where widetilde{C_i} = frac{1}{2} - left|frac{C_i}{M}- frac{1}{2} right| and delta_f = f(0)+f(M) - 2 f left( frac{M}{2} right).


, convex function, positive linear map, Jensen--Mercer operator inequality, Petrovi c operator inequality
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author = {Sal Moslehian, Mohammad and Jadranka Micic and Mohsen Kian},
title = {Operator inequalities of Jensen type},
journal = {Topological Algebra and its Applications},
year = {2013},
volume = {1},
number = {1},
month = {April},
issn = {2299-3231},
pages = {9--21},
numpages = {12},
keywords = {convex function; positive linear map; Jensen--Mercer operator inequality; Petrovi c operator inequality},


%0 Journal Article
%T Operator inequalities of Jensen type
%A Sal Moslehian, Mohammad
%A Jadranka Micic
%A Mohsen Kian
%J Topological Algebra and its Applications
%@ 2299-3231
%D 2013