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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. Kalinichenkoa, M. A. Plievb

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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\pages 38--45
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\pages 33--39
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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