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
@article{paperid:1039480,
author = {J.I. Fujii and M. Fujii and Sal Moslehian, Mohammad and Y. Seo},
title = {Cauchy--Schwarz inequality in semi-inner product C*-modules via polar decomposition},
journal = {Journal of Mathematical Analysis and Applications},
year = {2012},
volume = {394},
number = {2},
month = {December},
issn = {0022-247X},
pages = {835--840},
numpages = {5},
keywords = {Hilbert $C^*$-module; operator inequality; operator
geometric mean; positive operator; Kantorovich inequality},
}
%0 Journal Article
%T Cauchy--Schwarz inequality in semi-inner product C*-modules via polar decomposition
%A J.I. Fujii
%A M. Fujii
%A Sal Moslehian, Mohammad
%A Y. Seo
%J Journal of Mathematical Analysis and Applications
%@ 0022-247X
%D 2012
