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Mat. Sb., 2005, Volume 196, Number 11, Pages 3–32 (Mi msb1387)  

This article is cited in 2 scientific papers (total in 2 papers)

On approximation of flat Banach modules by free modules

O. Yu. Aristov

Obninsk State Technical University for Nuclear Power Engineering

Abstract: The local structure of flat Banach modules is considered; in particular, it is shown that if a flat module has the approximation property, then it is freely approximable, that is, the identity operator on it is approximated by operators each of which admits factorization through a free Banach module satisfying a natural finiteness condition. Among the maps involved in the factorization, the first is approximately multiplicative up to $\varepsilon$ on compact sets, and the second is exactly a morphism of modules. The properties of freely approximable and approximately projective modules are studied. It is proved that the standard complex for calculating the derived functor Ext is locally asymptotically exact in the first term for an arbitrary second argument if and only if its first argument is a flat Banach module.

DOI: https://doi.org/10.4213/sm1387

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English version:
Sbornik: Mathematics, 2005, 196:11, 1553–1583

Bibliographic databases:

UDC: 517.98
MSC: Primary 46H25; Secondary 16D40, 16D90, 46M07, 46M10, 46M18
Received: 10.08.2004 and 26.07.2005

Citation: O. Yu. Aristov, “On approximation of flat Banach modules by free modules”, Mat. Sb., 196:11 (2005), 3–32; Sb. Math., 196:11 (2005), 1553–1583

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pirkovskii A.Yu., “Approximate characterizations of projectivity and injectivity for Banach modules”, Math. Proc. Cambridge Philos. Soc., 143:2 (2007), 375–385  crossref  mathscinet  zmath  isi  elib
    2. H. Pourmahmood-Aghababa, “Approximately biprojective Banach algebras and nilpotent ideals”, Bull. Aust. Math. Soc, 2012, 1  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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