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σ-fragmented Banach spaces II

J. JayneI. NamiokaC. Rogers — 1994

Studia Mathematica

Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that...

Fragmentability and σ-fragmentability

J. JayneI. NamiokaC. Rogers — 1993

Fundamenta Mathematicae

Recent work has studied the fragmentability and σ-fragmentability properties of Banach spaces. Here examples are given that justify the definitions that have been used. The fragmentability and σ-fragmentability properties of the spaces and c ( Γ ) , with Γ uncountable, are determined.

Radon Measures on Banach Spaces with their Weak Topologies

Jayne, J.Rogers, C. — 1995

Serdica Mathematical Journal

The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.

Norm fragmented weak* compact sets.

J. E. JayneI. NamiokaC. A. Rogers — 1990

Collectanea Mathematica

A Banach space which is a Cech-analytic space in its weak topology has fourteen measure-theoretic, geometric and topological properties. In a dual Banach space with its weak-star topology essentially the same properties are all equivalent one to another.

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