Geodesic
Standard exact projective resolutions relative to a countable class of Fréchet spaces
Studia Mathematica, Tome 123 (1997) no. 3, pp. 275-290

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-123-3-275-290
Mots-clés : Fréchet spaces, Köthe sequence spaces, splitting of short exact sequences, nuclear spaces, Schwartz spaces, quasinormable spaces, functor $Ext^1$, projective spaces, projective resolution

P. Domański 1 ;  1 ;  1

1 
@article{10_4064_sm_123_3_275_290,
     author = {P. Doma\'nski and   and  },
     title = {Standard exact projective resolutions relative to a countable class of {Fr\'echet} spaces},
     journal = {Studia Mathematica},
     pages = {275--290},
     publisher = {mathdoc},
     volume = {123},
     number = {3},
     year = {1997},
     doi = {10.4064/sm-123-3-275-290},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-123-3-275-290/}
}
TY  - JOUR
AU  - P. Domański
AU  -  
AU  -  
TI  - Standard exact projective resolutions relative to a countable class of Fréchet spaces
JO  - Studia Mathematica
PY  - 1997
SP  - 275
EP  - 290
VL  - 123
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-123-3-275-290/
DO  - 10.4064/sm-123-3-275-290
LA  - fr
ID  - 10_4064_sm_123_3_275_290
ER  - 
%0 Journal Article
%A P. Domański
%A  
%A  
%T Standard exact projective resolutions relative to a countable class of Fréchet spaces
%J Studia Mathematica
%D 1997
%P 275-290
%V 123
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-123-3-275-290/
%R 10.4064/sm-123-3-275-290
%G fr
%F 10_4064_sm_123_3_275_290
P. Domański;  ;  . Standard exact projective resolutions relative to a countable class of Fréchet spaces. Studia Mathematica, Tome 123 (1997) no. 3, pp. 275-290. doi: 10.4064/sm-123-3-275-290

Cité par Sources :