Measures of weak noncompactness are formulae that quantify different characterizations of
weak compactness in Banach spaces: we deal here with De Blasi's measure ω and the …

We investigate possible quantifications of the Dunford–Pettis property. We show, in
particular, that the Dunford–Pettis property is automatically quantitative in a sense. Further …

We investigate possible quantifications of the Banach–Saks property and the weak Banach–
Saks property. We prove quantitative versions of relationships of the Banach–Saks property …

We introduce two measures of weak non-compactness JaE and Ja that quantify, via
distances, the idea of boundary that lies behind James's Compactness Theorem. These …

arXiv:1204.4308v1 [math.FA] 19 Apr 2012 Page 1 arXiv:1204.4308v1 [math.FA] 19 Apr 2012
QUANTIFICATION OF THE RECIPROCAL DUNFORD-PETTIS PROPERTY ONDREJ FK …

Non-convex functions that yet satisfy a condition of uniform convexity for non-close points
can arise in discrete constructions. We prove that this sort of discrete uniform convexity is …

We introduce a measure of super weak noncompactness Γ defined for bounded subsets and
bounded linear operators in Banach spaces that allows to state and prove a characterization …

A Banach space X is Grothendieck if the weak and the weak⁎ convergence of sequences in
the dual space X⁎ coincide. The space ℓ∞ is a classical example of a Grothendieck space …

We establish here some inequalities between distances of pointwise bounded subsets H of
RX to the space of real-valued continuous functions C (X) that allow us to examine the …

Given a metric space X and a Banach space (E,||·||) we use an index of σ-fragmentability for
maps f ∈ E^ X to estimate the distance of f to the space B 1 (X, E) of Baire one functions from …