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Inner characterizations of weakly compactly generated Banach spaces and their relatives

2004; Elsevier BV; Volume: 297; Issue: 2 Linguagem: Inglês

10.1016/j.jmaa.2004.02.015

1096-0813

Marián Fabian, Gilles Godefroy, V. Montesinos, Václav Zizler,

Approximation Theory and Sequence Spaces

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.