Journal of Mathematical Analysis and Applications, ( ISI ), Volume (394), No (2), Year (2012-12) , Pages (835-840)

Title : ( Cauchy--Schwarz inequality in semi-inner product C*-modules via polar decomposition )

Authors: J.I. Fujii , M. Fujii , Mohammad Sal Moslehian , Y. Seo ,

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Abstract

By virtue of the operator geometric mean and the polar decomposition, we present a new Cauchy--Schwarz inequality in the framework of semi-inner product $C^*$-modules over unital $C^*$--algebras and discuss the equality case. We also give several additive and multiplicative type reverses of it. As an application, we present a Kantorovich type inequality on a Hilbert $C^*$-module.

Keywords

, Hilbert $C^*$-module, operator inequality, operator geometric mean, positive operator, Kantorovich inequality