arXiv:math/0610420v2 [math.FA] 14 Oct 2006 Page 1 arXiv:math/0610420v2 [math.FA] 14 Oct
2006 LOCALLY UNIFORMLY CONVEX NORMS IN BANACH SPACES AND THEIR DUALS …

Recall that a Banach space X has the Radon–Nikodým (RN) property if and only if the
Radon–Nikodým theorem holds for vector measures with values in X (see [12]). This …

It is shown that most of the well known classes of nonseparable Banach spaces related to
the weakly compact generating can be characterized by elementary properties of the closure …

We list a number of problems in several topics related to compactness in nonseparable
Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous …

A compact space is said to be weakly Radon–Nikodým if it is homeomorphic to a weak*-
compact subset of the dual of a Banach space not containing an isomorphic copy of ℓ 1. In …

SOME EXAMPLES OF CONTINUOUS IMAGES OF RADON-NIKODÝM COMPACT SPACES 1.
Introduction This note contains some ideas to address the Page 1 Czechoslovak Mathematical …

We prove that every fragmentable linearly ordered compact space is almost totally
disconnected. This combined with a result of Arvanitakis yields that every linearly ordered …

We consider the cardinal invariant CG (X) of the minimal number of weakly compact subsets
which generate a Banach space X. We study the behavior of this index when passing to …

In the context of classical associations between classes of Banach spaces and classes of
compact Hausdorff spaces we survey known results and open questions concerning the …

The♢-principle, introduced by Jensen in 1972 ([Jen72]), became one of the most used
auxiliary axioms to ZFC. It has proven to be a powerful tool for many recursive constructions …