A new characterization of Eberlein compacta

Abstract

Abstract. We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.

Network characterization of Gul'ko compact spaces and their relatives

“…They have become a prominent tool in renorming theory after the seminal paper of Hansell [27], who showed that different kind of networks in Banach spaces are related to fragmentability properties [31]. The linking separability property (LSP, for short), is another tool we have used to connect networks for different metric spaces [32,34,35]. Dow et al [13] have characterized quite recently the LSP in terms of a network condition too.…”

“…Since the seminal paper by Amir and Lindenstrauss [1], where they showed the interplay between topological and geometrical properties of the so-called weakly compactly generated Banach spaces, a lot of research has been done on this class of Banach spaces and their relatives such as weakly K-analytic, weakly countably determined and weakly Lindelöf determined Banach spaces [3,8,16,26,34,35,38,39,42,44,45].…”