- Tytuł:
- Standard exact projective resolutions relative to a countable class of Fréchet spaces
- Autorzy:
-
Domański, P.
Krone, J.
Vogt, D. - Powiązania:
- https://bibliotekanauki.pl/articles/1220055.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Fréchet spaces
Köthe sequence spaces
splitting of short exact sequences
nuclear spaces
Schwartz spaces
quasinormable spaces
functor $Ext^1$
projective spaces
projective resolution - Opis:
- We will show that for each sequence of quasinormable Fréchet spaces $(E_n)_ℕ$ there is a Köthe space λ such that $Ext^1(λ(A), λ(A) = Ext^1 (λ(A), E_n)=0$ and there are exact sequences of the form $... → λ(A) → λ(A) → λ(A) → λ(A) → {E_n} → 0$. If, for a fixed ℕ, $E_n$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 → λ(A) → λ(A) → {E_n} → 0$. The result has some applications in the theory of the functor $Ext^1$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.
- Źródło:
-
Studia Mathematica; 1997, 123, 3; 275-290
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł