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Sbornik: Mathematics, 2020, Volume 211, Issue 10, Pages 1447–1459
DOI: https://doi.org/10.1070/SM9342 (Mi sm9342) 		 
Topologically projective, injective and flat modules of harmonic analysis

N. T. Nemesh

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.1070/SM9342
Abstract: We study homologically trivial modules of harmonic analysis on a locally compact group $G$. For $L_1(G)$- and $M(G)$-modules $C_0(G)$, $L_p(G)$ and $M(G)$ we give criteria for metric and topological projectivity, injectivity and flatness. In most cases, modules with these properties must be finite-dimensional.
Bibliography: 18 titles.
Keywords: Banach module, projectivity, injectivity, flatness, harmonic analysis.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00447-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 19-01-00447-a).
Received: 31.10.2019 and 29.12.2019
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 10, Pages 98–111
DOI: https://doi.org/10.4213/sm9342
Bibliographic databases:
Document Type: Article
UDC: 517.968.22
MSC: Primary 46M10; Secondary 28A05, 54G05
Language: English
Original paper language: Russian
Citation: N. T. Nemesh, “Topologically projective, injective and flat modules of harmonic analysis”, Mat. Sb., 211:10 (2020), 98–111; Sb. Math., 211:10 (2020), 1447–1459
Citation in format AMSBIB
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