Electronic Journal of Linear Algebra, ( ISI ), Volume (22), No (1), Year (2011-6) , Pages (179-190)

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