This is a commented collection of some easily formulated open problems in the geometry
and analysis on Banach spaces, focusing on basic linear geometry, convexity …

Given a compact space K, we denote by P (K) the space of all Radon probability measures
on K, equipped with the weak* topology inherited from C (K)*. For nonmetrizable compacta …

For a compact space $ K $, the Banach space $ C (K) $ is said to have the $\ell_1 $-
Grothendieck property if every weak* convergent sequence $\big\langle\mu_n\colon\n\in …

Given two Banach spaces X and Y, we analyze when the projective tensor product X⊗ ˆ π Y
has Corson's property (C) or is weakly Lindelöf determined (WLD), subspace of a weakly …

A well-known result of R. Pol states that a Banach space X has property (C) of Corson if and
only if every point in the weak*-closure of any convex set C⊆ BX⁎ is actually in the weak …

We construct a compact Hausdorff space KK such that the space P (K) P(K) of Radon
probability measures on KK considered with the weak∗ weak^* topology (induced from the …

A Boolean algebra A has the Nikodym property if every pointwise bounded sequence of
bounded finitely additive measures on A is uniformly bounded. Assuming the Diamond …

We study the class of compact spaces that appear as structure spaces of separable Banach
lattices. In other words, we analyze what C (K) spaces appear as principal ideals of …

Abstract Let (Ω, Σ, μ) be a complete probability space, X a Banach space and 1≤ p<∞. In
this paper we discuss several aspects of p-Dunford integrable functions f: Ω→ X. Special …

The celebrated Josefson-Nissenzweig theorem implies that for a Banach space $ C (K) $ of
continuous real-valued functions on an infinite compact space $ K $ there exists a sequence …