A Diaz--Metcalf type inequality for positive linear maps and its applications

Details A Diaz--Metcalf type inequality for positive linear maps and its applications A Diaz--Metcalf type inequality for positive linear maps and its applications

2011-02-27

arxiv.org/abs/1102.5492v1

Electron. J. Linear Algebra 22 (2011), 179-190

Mathematics

Functional Analysis

12 pages, to appear in Electronic Journal of Linear Algebra (ELA)

Scientific paper

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.

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