Geodesic
A new class of weakly $K$-analytic Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 291-312

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we define and investigate a new subclass of those Banach spaces which are $K$-analytic in their weak topology; we call them strongly weakly $K$-analytic (SWKA) Banach spaces. The class of SWKA Banach spaces extends the known class of strongly weakly compactly generated (SWCG) Banach spaces (and their subspaces) and it is related to that in the same way as the familiar classes of weakly $K$-analytic (WKA) and weakly compactly generated (WCG) Banach spaces are related. We show that: (i) not every separable Banach space is SWKA; (ii) every separable SWKA Banach space not containing $\ell^1$ is Polish; (iii) we answer in the negative a question posed in [S-W] by constructing a subspace $X$ of the SWCG space $L^1[0,1]$ which is not SWCG.
Classification : 03E15, 03E75, 46B20, 46B26, 54H05
Keywords: WKA; SWKA Banach spaces; $K$-analytic space; Baire space; Polish space 
@article{CMUC_2006__47_2_a7,
     author = {Mercourakis, S. and Stamati, E.},
     title = {A new class of weakly $K$-analytic {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {291--312},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2006},
     mrnumber = {2241533},
     zbl = {1150.46008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a7/}
}
TY  - JOUR
AU  - Mercourakis, S.
AU  - Stamati, E.
TI  - A new class of weakly $K$-analytic Banach spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 291
EP  - 312
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a7/
LA  - en
ID  - CMUC_2006__47_2_a7
ER  - 
%0 Journal Article
%A Mercourakis, S.
%A Stamati, E.
%T A new class of weakly $K$-analytic Banach spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 291-312
%V 47
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a7/
%G en
%F CMUC_2006__47_2_a7
Mercourakis, S.; Stamati, E. A new class of weakly $K$-analytic Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 291-312. http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a7/