Annals of Functional Analysis

Hölder type inequalities on Hilbert $C^*$-modules and its reverses

Yuki Seo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we show Hilbert $C^*$-module versions of Hölder--McCarthy inequality and its complementary inequality. As an application, we obtain Hölder type inequalities and its reverses on a Hilbert $C^*$-module.

Article information

Source
Ann. Funct. Anal., Volume 5, Number 1 (2014), 1-9.

Dates
First available in Project Euclid: 5 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1391614563

Digital Object Identifier
doi:10.15352/afa/1391614563

Mathematical Reviews number (MathSciNet)
MR3119106

Zentralblatt MATH identifier
1296.46051

Subjects
Primary: 46L08: $C^*$-modules
Secondary: 47A63: Operator inequalities 47A64: Operator means, shorted operators, etc.

Keywords
Hölder-McCarthy inequality Hölder inequality Hilbert $C^*$-module geometric operator mean

Citation

Seo, Yuki. Hölder type inequalities on Hilbert $C^*$-modules and its reverses. Ann. Funct. Anal. 5 (2014), no. 1, 1--9. doi:10.15352/afa/1391614563. https://projecteuclid.org/euclid.afa/1391614563


Export citation

References

  • T. Ando, Concavity of certain maps on positive matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203-241.
  • T. Ando and F. Hiai, Hölder type inequalities for matrices, Math. Inequal. Appl. 1 (1988), 1-30.
  • J.-C. Bourin, E.-Y. Lee, M. Fujii and Y. Seo, A matrix reverse Hölder inequality, Linear Algegra Appl. 431 (2009), 2154–2159.
  • M.D. Choi, A Schwarz inequality for positive linear maps on $C^*$-algebras, Illinois J. Math. 18 (1974), 565–574.
  • Ch. Davis, A Schwartz inequality for convex operator functions, Proc. Amer. Math. Soc. 8 (1957), 42–44.
  • J.I. Fujii, M. Fujii, M.S. Moslehian and Y. Seo, Cauchy–Schwarz inequality in semi-inner product $C^*$-modules via polar decomposition, J. Math. Anal. Appl. 394 (2012), 835-840.
  • M. Fujii, S. Izumino, R. Nakamoto and Y. Seo, Operator inequalities related to Cauchy–Schwarz and Hölder–McCarthy inequalities, Nihonkai Math. J. 8 (1997), 117–122.
  • J.I. Fujii, M. Fujii and Y. Seo, Operator inequalities on Hilbert $C^*$-modules via the Cauchy–Schwarz inequality, Math. Inequal. Appl. (to appear).
  • T. Furuta, Invitation to Linear Operators, Taylor& Francis, London, 2001.
  • T. Furuta, J. Mićić Hot, J. Pečarić and Y. Seo, Mond-Pečarić Method in Operator Inequalities, Monographs in Inequalities 1, Element, Zagreb, 2005.
  • S. Izumino and M. Tominaga, Estimations in Hölder type inequalities, Math. Inequal. Appl. 4 (2001), 163–187.
  • F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246 (1980), 205–224.
  • E.C. Lance, Hilbert $C^*$-Modules, London Math. Soc. Lecture Note Series 210, Cambridge Univ. Press, 1995.
  • V.M. Manuilov and E.V. Troitsky, Hilbert $C^*$-Modules, Translations of Mathematical Monographs, 226, American Mathematical Society, Providence RI, 2005.
  • B. Mond and O. Shisha, Difference and ratio inequalities in Hilbert space. Inequalities II, (O.Shisha, ed.), Academic Press, New York, 1970, 241–249.
  • W.L. Paschke, Inner product modules over $B^*$-algebras, Trans. Amer. Math. Soc. 182 (1973), 443–468.