Geodesic
Some remarks on quasi-Cohen sets
Pascal Lefèvre1 ; Daniel Li2
1 Faculté Jean Perrin Université d'Artois rue Jean Souvraz S.P. 18 62307 Lens Cedex, France
2 Faculté Jean Perrin Université d'Artois rue Jean Souvraz S.P. 18 62307 Lens Cedex
Colloquium Mathematicum, Tome 89 (2001) no. 2, pp. 169-178.

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

We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets $E$ of the dual of an abelian compact group $G$ such that the canonical injection $C(G)/C_{E^{\rm c}}(G)\hookrightarrow L^2_E(G)$ is a $2$-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of $L^1$ which are isomorphic to subspaces of $L^1$.
DOI : 10.4064/cm89-2-2
Keywords: interested banach space geometry characterizations quasi cohen sets example turns out exactly subsets dual abelian compact group canonical injection hookrightarrow summing operator easily yields extension result due kwapie czy ski investigate properties translation invariant quotients which isomorphic subspaces

Pascal Lefèvre 1 ; Daniel Li 2

1 Faculté Jean Perrin Université d'Artois rue Jean Souvraz S.P. 18 62307 Lens Cedex, France
2 Faculté Jean Perrin Université d'Artois rue Jean Souvraz S.P. 18 62307 Lens Cedex 
@article{10_4064_cm89_2_2,
     author = {Pascal Lef\`evre and Daniel Li},
     title = {Some remarks on {quasi-Cohen} sets},
     journal = {Colloquium Mathematicum},
     pages = {169--178},
     publisher = {mathdoc},
     volume = {89},
     number = {2},
     year = {2001},
     doi = {10.4064/cm89-2-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm89-2-2/}
}
TY  - JOUR
AU  - Pascal Lefèvre
AU  - Daniel Li
TI  - Some remarks on quasi-Cohen sets
JO  - Colloquium Mathematicum
PY  - 2001
SP  - 169
EP  - 178
VL  - 89
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm89-2-2/
DO  - 10.4064/cm89-2-2
LA  - en
ID  - 10_4064_cm89_2_2
ER  - 
%0 Journal Article
%A Pascal Lefèvre
%A Daniel Li
%T Some remarks on quasi-Cohen sets
%J Colloquium Mathematicum
%D 2001
%P 169-178
%V 89
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm89-2-2/
%R 10.4064/cm89-2-2
%G en
%F 10_4064_cm89_2_2
Pascal Lefèvre; Daniel Li. Some remarks on quasi-Cohen sets. Colloquium Mathematicum, Tome 89 (2001) no. 2, pp. 169-178. doi : 10.4064/cm89-2-2. http://geodesic.mathdoc.fr/articles/10.4064/cm89-2-2/

Cité par Sources :