Banach Journal of Mathematical Analysis

On the Cauchy-Schwarz inequality and its reverse in semi-inner product C*-modules

Dijana Ilisevic and Sanja Varosanec

Full-text: Open access

Abstract

There are many known Cauchy-Schwarz-type inequalities which are valid in different frameworks. In this paper we consider the $A$-valued Cauchy-Schwarz inequality and its reverse in a semi-inner product $A$-module over the $C^*$-algebra $A$. Some remarks on the $A$-valued Cauchy-Schwarz inequality in a semi-inner product $A$-module over the $H^*$-algebra $A$ are also given.

Article information

Source
Banach J. Math. Anal. Volume 1, Number 1 (2007), 78-84.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240321557

Digital Object Identifier
doi:10.15352/bjma/1240321557

Mathematical Reviews number (MathSciNet)
MR2350196

Zentralblatt MATH identifier
1134.46036

Subjects
Primary: 46L08: $C^*$-modules
Secondary: 26D07: Inequalities involving other types of functions

Keywords
the Cauchy-Schwarz inequality semi-inner product C*-module semi-inner product H*-module

Citation

Ilisevic, Dijana; Varosanec, Sanja. On the Cauchy-Schwarz inequality and its reverse in semi-inner product C*-modules. Banach J. Math. Anal. 1 (2007), no. 1, 78--84. doi:10.15352/bjma/1240321557. https://projecteuclid.org/euclid.bjma/1240321557


Export citation

References

  • S.S. Dragomir, A counterpart of Schwarz's inequality in inner product spaces, RGMIA Res. Rep. Coll. 6 (2003), Supplement, Article 18 [http://rgmia.vu.edu.au/v6(E).html]
  • D. Ilišević, Quadratic functionals on modules over complex Banach $\ast$-algebras with an approximate identity, Studia Math. 171 (2005), 103–123.
  • E.C. Lance, Hilbert $C^*$-modules. A Toolkit for Operator Algebraists, London Math. Soc. Lecture Series, 210. Cambridge University Press, Cambridge, 1995.
  • G.J. Murphy, $C^*$-Algebras and Operator Theory, Academic Press, Boston, 1990.
  • Th.M. Rassias, Survey on Classical Inequalities, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000.
  • Th.M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, Boston, London, 2003.
  • J.F. Smith, The $p$-classes of an $H^*$-algebra, Pacific J. Math. 42 (1972), 777–793.