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Inner characterizations of weakly compactly generated Banach spaces and their relatives |
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| Authors: | M. Fabian G. Godefroy V. Zizler |
| Affiliation: | a Mathematical Institute of the Czech Academy of Sciences, ?itná 25, 11567, Prague 1, Czech Republic b Equipe d'analyse, Université Paris VI, Case 186, 4 Place Jussieu, 75252 Paris cedex 05, France c Departamento de Matemática Aplicada, ETSI Telecomunicación, Universidad Politécnica de Valencia, C/Vera, s/n. 46071 Valencia, Spain d Department of Mathematical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, Alberta, Canada T6G 2G1 |
| Abstract: | We give characterizations of weakly compactly generated spaces, their subspaces, Vašák spaces, weakly Lindelöf determined spaces as well as several other classes of Banach spaces related to uniform Gâteaux smoothness, in terms of the presence of a total subset of the space with some additional properties. In addition, we describe geometrically, when possible, these classes by means of suitable smoothness or rotundity of the norm. As a consequence, we get new, functional analytic proofs of several theorems on (uniform) Eberlein, Gul'ko and Talagrand compacta. |
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