Annals of Functional Analysis

Advances in Operator Cauchy--Schwarz inequalities and their reverses

J. M. Aldaz, S. Barza, M. Fujii, and M. S. Moslehian

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The Cauchy-Schwarz (C-S) inequality is one of the most famous inequalities in mathematics. In this survey article, we first give a brief history of the inequality. Afterward, we present the C-S inequality for inner product spaces. Focusing on operator inequalities, we then review some significant recent developments of the C-S inequality and its reverses for Hilbert space operators and elements of Hilbert $C^*$-modules. In particular, we pay special attention to an operator Wielandt inequality.

Article information

Ann. Funct. Anal., Volume 6, Number 3 (2015), 275-295.

First available in Project Euclid: 17 April 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 46L05: General theory of $C^*$-algebras 47A30: Norms (inequalities, more than one norm, etc.) 26D15: Inequalities for sums, series and integrals

History of mathematics Operator inequality operator geometric mean Cauchy--Schwarz inequality


Aldaz, J. M.; Barza, S.; Fujii, M.; Moslehian, M. S. Advances in Operator Cauchy--Schwarz inequalities and their reverses. Ann. Funct. Anal. 6 (2015), no. 3, 275--295. doi:10.15352/afa/06-3-20.

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