Open Access
2008 Operator-valued inner product and operator inequalities
Jun Ichi Fujii
Banach J. Math. Anal. 2(2): 59-67 (2008). DOI: 10.15352/bjma/1240336292


The Schwarz inequality and Jensen's one are fundamental in a Hilbert space. Regarding a sesquilinear map $B(X,Y)=Y^*X$ as an operator-valued inner product, we discuss operator versions for the above inequalities and give simple conditions that the equalities hold.


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Jun Ichi Fujii. "Operator-valued inner product and operator inequalities." Banach J. Math. Anal. 2 (2) 59 - 67, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1151.47024
MathSciNet: MR2404103
Digital Object Identifier: 10.15352/bjma/1240336292

Primary: 47A63
Secondary: 47A75 , 47A80

Keywords: Jensen inequality , ‎operator inequality , Schwarz inequality

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 2 • 2008
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