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The Triangle Equality in Hilbert A-modules

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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∣.

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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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Authors and Affiliations

  1. North-Caucasian Institute of Mining and Metallurgy, State Technological University, 44 Nikolaeva str., Vladikavkaz, 362021, Russia

    A. V. Kalinichenko

  2. Southern Mathematical Institute of the Russian Academy of Sciences, 22 Markusa str., Vladikavkaz, 362027, Russia

    M. A. Pliev

Authors
  1. A. V. Kalinichenko
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  2. M. A. Pliev
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Corresponding authors

Correspondence to A. V. Kalinichenko or M. A. Pliev.

Additional information

Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 10, pp. 38–45.

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Kalinichenko, A.V., Pliev, M.A. The Triangle Equality in Hilbert A-modules. Russ Math. 63, 33–39 (2019). https://doi.org/10.3103/S1066369X19100050

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  • DOI: https://doi.org/10.3103/S1066369X19100050

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