Hokkaido Mathematical Journal

FUJII Jun-Ichi, FUJII Masatoshi, MOSLEHIAN Mohammad Sal, PEČARIĆ Josip E., SEO Yuki,

Reverse Cauchy-Schwarz type inequalities in pre-inner product C*-modules.

Hokkaido Mathematical Journal, 40 (2011) pp.393-409

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Abstract

In the framework of a pre-inner product C*-module over a unital C*-algebra, we show several reverse Cauchy-Schwarz type inequalities of additive and multiplicative types, by using some ideas in N. Elezović et al. [Math. Inequal. Appl., 8 (2005), no.2, 223-231]. We apply our results to give Klamkin-Mclenaghan, Shisha-Mond and Cassels type inequalities. We also present a Grüss type inequality.

MSC(Primary)46L08
MSC(Secondary)26D15, 46L05, 47A30, 47A63
Uncontrolled KeywordsC*-algebra, reverse Cauchy-Schwarz inequality, pre-inner product C*-module, Cassels' inequality, operator geometric mean, operator inequality