Standard exact projective resolutions relative to a countable class of Fréchet spaces
Authors:
- Paweł Jan Domański,
- J. Krone,
- D. Vogt
Abstract
We will show that for each sequence of quasinormable Fréchet spaces (En)n∈ℕ there is a Köthe space λ(A) such that Ext1(λ(A), λ(A)) = Ext1(λ(A), En) = 0 and there are exact sequences of the form . . . → λ(A) → λ(A) → λ(A) → λ(A) → En → 0. If, for a fixed n ∈ ℕ, En is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form 0 → λ(A) → λ(A) → En → 0. The result has some applications in the theory of the functor Ext1 in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
- Record ID
- UAM3034693c4f2643099d44295db0926c64
- Author
- Journal series
- Studia Mathematica, ISSN 0039-3223
- Issue year
- 1997
- Vol
- 123
- Pages
- 275-290
- ASJC Classification
- Language
- (en) English
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 1; : 1999 = 1.135; : 2006 (2 years) = 0.515 - 2007 (5 years) =0.673
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- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAM3034693c4f2643099d44295db0926c64/
- URN
urn:amu-prod:UAM3034693c4f2643099d44295db0926c64
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