Title : ( A Diaz-Metcalf type inequality for positive linear maps and its applications )
Authors: Mohammad Sal Moslehian , Ritsuo Nakamoto , Yuki Seo ,
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Abstract
We present a Diaz--Metcalf type operator inequality as a reverse Cauchy--Schwarz inequality and then apply it to get the operator versions of P {o}lya--Szeg {o} s, Greub--Rheinboldt s, Kantorovich s, Shisha--Mond s, Schweitzer s, Cassels and Klamkin--McLenaghan s inequalities via a unified approach. We also give some operator Gr uss type inequalities and an operator Ozeki--Izumino--Mori--Seo type inequality. Several applications are concluded as well.
Keywords
, Diaz--Metcalf type inequality, reverse Cauchy--Schwarz inequality, positive map, Ozeki--Izumino--Mori--Seo inequality, operator inequality
@article{paperid:1020258,
author = {Sal Moslehian, Mohammad and Ritsuo Nakamoto and Yuki Seo},
title = {A Diaz-Metcalf type inequality for positive linear maps and its applications},
journal = {Electronic Journal of Linear Algebra},
year = {2011},
volume = {22},
number = {1},
month = {June},
issn = {1537-9582},
pages = {179--190},
numpages = {11},
keywords = {Diaz--Metcalf type inequality; reverse Cauchy--Schwarz inequality; positive map; Ozeki--Izumino--Mori--Seo inequality; operator inequality},
}
%0 Journal Article
%T A Diaz-Metcalf type inequality for positive linear maps and its applications
%A Sal Moslehian, Mohammad
%A Ritsuo Nakamoto
%A Yuki Seo
%J Electronic Journal of Linear Algebra
%@ 1537-9582
%D 2011
