Title : ( Bellman inequality for Hilbert space operators )
Authors: Ali Morassaei , Farazollah Mirzapour , Mohammad Sal Moslehian ,
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Abstract
We establish some operator versions of Bellman s inequality. In particular, we prove that if Phi: mathbb{B}( mathscr{H}) to mathbb{B}( mathscr{K}) is a unital positive linear map, A,B in mathbb{B}( mathscr{H})$ are contractions, p>1 and 0 leq lambda leq 1 , then begin{eqnarray*} big( Phi(I_ mathscr{H}-A nabla_{ lambda}B) big)^{1/p} ge Phi big((I_ mathscr{H}-A)^{1/p} nabla_{ lambda}(I_ mathscr{H}-B)^{1/p} big). end{eqnarray*}
Keywords
, Bellman inequality, Operator arithmetic mean, Operator concave, Operator decreasing, Positive linear functional
@article{paperid:1037799,
author = {Ali Morassaei and Farazollah Mirzapour and Sal Moslehian, Mohammad},
title = {Bellman inequality for Hilbert space operators},
journal = {Linear Algebra and its Applications},
year = {2013},
volume = {438},
number = {10},
month = {April},
issn = {0024-3795},
pages = {3776--3780},
numpages = {4},
keywords = {Bellman inequality; Operator arithmetic mean; Operator concave; Operator decreasing; Positive linear functional},
}
%0 Journal Article
%T Bellman inequality for Hilbert space operators
%A Ali Morassaei
%A Farazollah Mirzapour
%A Sal Moslehian, Mohammad
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2013
