Hokkaido Mathematical Journal

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

Jun-Ichi FUJII, Masatoshi FUJII, Mohammad Sal MOSLEHIAN, Josip E. PEČARIĆ, and Yuki SEO

Full-text: Open access

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.

Article information

Source
Hokkaido Math. J., Volume 40, Number 3 (2011), 393-409.

Dates
First available in Project Euclid: 26 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1319595863

Digital Object Identifier
doi:10.14492/hokmj/1319595863

Mathematical Reviews number (MathSciNet)
MR2883498

Zentralblatt MATH identifier
1267.46074

Subjects
Primary: 46L08: $C^*$-modules
Secondary: 26D15: Inequalities for sums, series and integrals 46L05: General theory of $C^*$-algebras 47A30: Norms (inequalities, more than one norm, etc.) 47A63: Operator inequalities

Keywords
C*-algebra reverse Cauchy-Schwarz inequality pre-inner product C*-module Cassels' inequality operator geometric mean operator inequality

Citation

FUJII, Jun-Ichi; FUJII, Masatoshi; MOSLEHIAN, Mohammad Sal; PEČARIĆ, Josip E.; SEO, Yuki. Reverse Cauchy-Schwarz type inequalities in pre-inner product C * -modules. Hokkaido Math. J. 40 (2011), no. 3, 393--409. doi:10.14492/hokmj/1319595863. https://projecteuclid.org/euclid.hokmj/1319595863


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