Geodesic
Smoothability, Strong Smoothability and Dentability in Banach Spaces1
Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 59-68

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

DOI

It is shown that dentability of the unit ball of a conjugate Banach space X* does not imply smoothability of the unit ball of X, answering a question raised by Kemp. A property called strong smoothability is introduced and is shown to be dual to dentability. The results are used to provide new proofs of the facts that X is an Asplund space whenever it has an equivalent Fréchet differentiable norm, or whenever X* has the Radon-Nikodym Property. 
Anantharaman, R.; Lewis, T.; Whitfield, J. H. M. Smoothability, Strong Smoothability and Dentability in Banach Spaces1. Canadian mathematical bulletin, Tome 24 (1981) no. 1, pp. 59-68. doi: 10.4153/CMB-1981-009-9
@article{10_4153_CMB_1981_009_9,
     author = {Anantharaman, R. and Lewis, T. and Whitfield, J. H. M.},
     title = {Smoothability, {Strong} {Smoothability} and {Dentability} in {Banach} {Spaces1}},
     journal = {Canadian mathematical bulletin},
     pages = {59--68},
     year = {1981},
     volume = {24},
     number = {1},
     doi = {10.4153/CMB-1981-009-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-009-9/}
}
TY  - JOUR
AU  - Anantharaman, R.
AU  - Lewis, T.
AU  - Whitfield, J. H. M.
TI  - Smoothability, Strong Smoothability and Dentability in Banach Spaces1
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 59
EP  - 68
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-009-9/
DO  - 10.4153/CMB-1981-009-9
ID  - 10_4153_CMB_1981_009_9
ER  - 
%0 Journal Article
%A Anantharaman, R.
%A Lewis, T.
%A Whitfield, J. H. M.
%T Smoothability, Strong Smoothability and Dentability in Banach Spaces1
%J Canadian mathematical bulletin
%D 1981
%P 59-68
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-009-9/
%R 10.4153/CMB-1981-009-9
%F 10_4153_CMB_1981_009_9

Cité par Sources :