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Russian Mathematics

, Volume 63, Issue 10, pp 33–39 | Cite as

The Triangle Equality in Hilbert A-modules

  • A. V. KalinichenkoEmail author
  • M. A. PlievEmail author
Article
  • 3 Downloads

Abstract

We show that for any two elements x, y of a Hilbert A-module M over a locally C*-algebra A the generalized triangle equality ∣x + y∣ = ∣x∣ + ∣y∣ holds if and only if 〈x, y〉 = ∣x∣∣y∣.

Key words

locally C*-algebra Hilbert A-module locally Hilbert space module compact operator *-homomorphism triangle equality 

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Notes

Acknowledgments

The authors are sincerely grateful to the anonymous referee for a careful reading of the text and the valuable remarks.

Funding

M.A. Pliev is supported by the grant of Russian Foundation for Basic Research 17-51-12064.

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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.North-Caucasian Institute of Mining and MetallurgyState Technological UniversityVladikavkazRussia
  2. 2.Southern Mathematical Institute of the Russian Academy of SciencesVladikavkazRussia

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