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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 5, Pages 55–63
DOI: https://doi.org/10.26907/0021-3446-2021-5-55-63 (Mi ivm9676) 		 
Hilbert $C^*$-modules related to discrete metric spaces

V. M. Manuilov

Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 1 Leninskie Gory, Moscow, 119991 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-5-55-63
Abstract: It is shown that a metric on the union of the sets $X$ and $Y$ determines a Hilbert $C^*$-module over the uniform Roe algebra of the space $X$. Several examples of such Hilbert $C^*$-modules are described in detail.
Keywords: metric space, Roe algebra, $C^*$-algebra, Hilbert $C^*$-module.
Funding agency Grant number
Russian Science Foundation 21-11-00080
Received: 20.03.2021
Revised: 20.03.2021
Accepted: 30.03.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 5, Pages 40–47
DOI: https://doi.org/10.3103/S1066369X21050078
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: V. M. Manuilov, “Hilbert $C^*$-modules related to discrete metric spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 5, 55–63; Russian Math. (Iz. VUZ), 65:5 (2021), 40–47
Citation in format AMSBIB
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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