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Funktsional'nyi Analiz i ego Prilozheniya, 2022, Volume 56, Issue 1, Pages 94–105
DOI: https://doi.org/10.4213/faa3921 (Mi faa3921) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A Hilbert $C^*$-modules with extremal properties

D. V. Fufaevab

a Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/faa3921
Abstract: We construct an example of a Hilbert $C^*$-module which shows that Troitsky's theorem on the geometric essence of $\mathcal{A}$-compact operators between Hilbert $C^*$-modules cannot be extended to modules which are not countably generated case (even in the case of a stronger uniform structure, which is also introduced). In addition, the constructed module admits no frames.
Keywords: Hilbert $C^*$-module, uniform structure, totally bounded set, compact operator, $\mathcal{A}$-compact operator, locally compact space, Radon measure.
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS
The work was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS.”
Received: 18.06.2021
Revised: 18.06.2021
Accepted: 20.08.2021
Published: 25.01.2022
English version:
Functional Analysis and Its Applications, 2022, Volume 56, Issue 1, Pages 72–80
DOI: https://doi.org/10.1134/S0016266322010075
Bibliographic databases:
Document Type: Article
UDC: 515.122+517.986.32
Language: Russian
Citation: D. V. Fufaev, “A Hilbert $C^*$-modules with extremal properties”, Funktsional. Anal. i Prilozhen., 56:1 (2022), 94–105; Funct. Anal. Appl., 56:1 (2022), 72–80
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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