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.
2004 Elsevier Inc. All rights reserved
