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This article is cited in 7 scientific papers (total in 7 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.
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
Linking options:
https://www.mathnet.ru/eng/sm1387https://doi.org/10.1070/SM2005v196n11ABEH003721 https://www.mathnet.ru/eng/sm/v196/i11/p3
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Abstract page: | 428 | Russian version PDF: | 224 | English version PDF: | 19 | References: | 31 | First page: | 1 |
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