RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

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

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

Full text: PDF file (458 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

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
\Bibitem{Ari05} \by O.~Yu.~Aristov \paper On approximation of flat Banach modules by free modules \jour Mat. Sb. \yr 2005 \vol 196 \issue 11 \pages 3--32 \mathnet{http://mi.mathnet.ru/msb1387} \crossref{https://doi.org/10.4213/sm1387} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216008} \zmath{https://zbmath.org/?q=an:1153.46030} \elib{https://elibrary.ru/item.asp?id=9154700} \transl \jour Sb. Math. \yr 2005 \vol 196 \issue 11 \pages 1553--1583 \crossref{https://doi.org/10.1070/SM2005v196n11ABEH003721} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000235973300001} \elib{https://elibrary.ru/item.asp?id=14333122} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645160006} 

• http://mi.mathnet.ru/eng/msb1387
• https://doi.org/10.4213/sm1387
• http://mi.mathnet.ru/eng/msb/v196/i11/p3

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. H. Pourmahmood-Aghababa, “Approximately biprojective Banach algebras and nilpotent ideals”, Bull. Aust. Math. Soc, 2012, 1
•  Number of views: This page: 312 Full text: 139 References: 21 First page: 1