Geodesic
A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact
Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 125-128

Voir la notice de l'article provenant de la source Cambridge University Press

A set D in a Banach space E is called limited if pointwise convergent sequences of linear functionals converge uniformly on D and E is called a GP-space (after Gelfand and Phillips) if every limited set in E is relatively compact. Banach spaces with weak * sequentially compact dual balls (W*SCDB for short) are GP-spaces and l1 is a GP-space without W*SCDB. Disproving a conjecture of Rosenthal and inspired by James tree space, Hagler and Odell constructed a class of Banach spaces ([HO]-spaces) without both W*SCDB and subspaces isomorphic to l1. Schlumprecht has shown that there is a subclass of the [HO]-spaces which are also GP-spaces. It is not clear however if any [HO]-construction yields a GP-space—in fact it is not even clear that W*SCDB[lrarr ]GP-space is false in general for the class of Banach spaces containing no subspace isomorphic to l1. In this note the example of Hagler and Odell is modified to yield a GP-space without W*SCDB and without an isomorphic copy of l1. 
Josefson, Bengt. A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact. Glasgow mathematical journal, Tome 43 (2001) no. 1, pp. 125-128. doi: 10.1017/S0017089501010114
@article{10_1017_S0017089501010114,
     author = {Josefson, Bengt},
     title = {A {Gelfand-Phillips} space not containing l1 whose dual ball is not weak * sequentially compact},
     journal = {Glasgow mathematical journal},
     pages = {125--128},
     year = {2001},
     volume = {43},
     number = {1},
     doi = {10.1017/S0017089501010114},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501010114/}
}
TY  - JOUR
AU  - Josefson, Bengt
TI  - A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact
JO  - Glasgow mathematical journal
PY  - 2001
SP  - 125
EP  - 128
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089501010114/
DO  - 10.1017/S0017089501010114
ID  - 10_1017_S0017089501010114
ER  - 
%0 Journal Article
%A Josefson, Bengt
%T A Gelfand-Phillips space not containing l1 whose dual ball is not weak * sequentially compact
%J Glasgow mathematical journal
%D 2001
%P 125-128
%V 43
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089501010114/
%R 10.1017/S0017089501010114
%F 10_1017_S0017089501010114

Cité par Sources :