A. V. Kalinichenko, M. A. Pliev, “The triangle equality in Hilbert $A$-modules”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 38–45; Russian Math. (Iz. VUZ), 63:10 (2019), 33

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 10, Pages 38–45
DOI: https://doi.org/10.26907/0021-3446-2019-10-38-45 (Mi ivm9505)

The triangle equality in Hilbert

$A$ -modules

A. V. Kalinichenko^a, M. A. Pliev^b

^a North-Caucasian Institute of Mining and Metallurgy (State Technological University), 44 Nikolaeva str., Vladikavkaz, 362021 Russia
^b Southern Mathematical Institute of the Russian Academy of Sciences, 22 Markusa str., Vladikavkaz, 362027 Russia

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DOI: https://doi.org/10.26907/0021-3446-2019-10-38-45

Abstract: We show that for any two elements

$x$ ,

$y$ of Hilbert

$A$ -module

$M$ over local

$C^*$ -algebra

$A$ the generalized triangle equality

$|x+y|=|x|+|y|$ holds if and only if

$\langle x,y\rangle=|x||y|$ .

Keywords: local

$C^{\ast}$ -algebra, Hilbert

$A$ -module, local Hilbert space, module compact operator,

$\ast$ -homomorphism, triangle equality.

Funding agency	Grant number
Russian Foundation for Basic Research	17-51-12064_ННИО_а

Received: 29.08.2018
Revised: 29.08.2018
Accepted: 19.12.2018

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 10, Pages 33–39
DOI: https://doi.org/10.3103/S1066369X19100050

Bibliographic databases:

Document Type: Article

UDC: 517.98: 519.46

Language: Russian

Citation: A. V. Kalinichenko, M. A. Pliev, “The triangle equality in Hilbert

$A$ -modules”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 38–45; Russian Math. (Iz. VUZ), 63:10 (2019), 33–39

Citation in format AMSBIB

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\paper The triangle equality in Hilbert $A$-modules

\jour Izv. Vyssh. Uchebn. Zaved. Mat.

\yr 2019

\issue 10

\pages 38--45

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\crossref{https://doi.org/10.26907/0021-3446-2019-10-38-45}

\transl

\jour Russian Math. (Iz. VUZ)

\yr 2019

\vol 63

\issue 10

\pages 33--39

\crossref{https://doi.org/10.3103/S1066369X19100050}

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https://www.mathnet.ru/eng/ivm9505

https://www.mathnet.ru/eng/ivm/y2019/i10/p38

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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