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

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.