Geodesic
On non-primary Fréchet Schwartz spaces
Studia Mathematica, Tome 126 (1997) no. 3, pp. 291-307

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

Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions of bounded type $ℋ_b(U)$, where U is a Banach space or a bounded absolutely convex open set in a Banach space.
DOI : 10.4064/sm-126-3-291-307
Mots-clés : Fréchet spaces, primary spaces, Schwartz spaces, unconditional decompositions, spaces of Moscatelli type, holomorphic functions of bounded type

J. C. Díaz 1

1 
@article{10_4064_sm_126_3_291_307,
     author = {J. C.  D{\'\i}az},
     title = {On non-primary {Fr\'echet} {Schwartz} spaces},
     journal = {Studia Mathematica},
     pages = {291--307},
     publisher = {mathdoc},
     volume = {126},
     number = {3},
     year = {1997},
     doi = {10.4064/sm-126-3-291-307},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-126-3-291-307/}
}
TY  - JOUR
AU  - J. C.  Díaz
TI  - On non-primary Fréchet Schwartz spaces
JO  - Studia Mathematica
PY  - 1997
SP  - 291
EP  - 307
VL  - 126
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-126-3-291-307/
DO  - 10.4064/sm-126-3-291-307
LA  - fr
ID  - 10_4064_sm_126_3_291_307
ER  - 
%0 Journal Article
%A J. C.  Díaz
%T On non-primary Fréchet Schwartz spaces
%J Studia Mathematica
%D 1997
%P 291-307
%V 126
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-126-3-291-307/
%R 10.4064/sm-126-3-291-307
%G fr
%F 10_4064_sm_126_3_291_307
J. C.  Díaz. On non-primary Fréchet Schwartz spaces. Studia Mathematica, Tome 126 (1997) no. 3, pp. 291-307. doi: 10.4064/sm-126-3-291-307

Cité par Sources :