Displaying similar documents to “Kadec norms and Borel sets in a Banach space”

The JNR Property and the Borel Structure of a Banach Space

Oncina, L. (2000)

Serdica Mathematical Journal

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Research partially supported by a grant of Caja de Ahorros del Mediterraneo. In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of...

Norm fragmented weak* compact sets.

J. E. Jayne, I. Namioka, C. A. Rogers (1990)

Collectanea Mathematica

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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.

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

Bossard, Benoit, López, Ginés (1998)

Serdica Mathematical Journal

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∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142 Let X be a separable Banach space without the Point of Continuity Property. When the set of closed subsets of its closed unit ball is equipped with the standard Effros-Borel structure, the set of those which have the Point of Continuity Property is non-Borel. We also prove that, for any separable Banach space X, the oscillation rank of the identity on X (an ordinal index which quantifies the Point of Continuity Property) is determined...

On the complexity of some classes of Banach spaces and non-universality

Bruno M. Braga (2014)

Czechoslovak Mathematical Journal

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These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded...

Descriptive Sets and the Topology of Nonseparable Banach Spaces

Hansell, R. (2001)

Serdica Mathematical Journal

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This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.

Some results in representable Banach spaces.

Miguel Angel Canela (1988)

Publicacions Matemàtiques

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Some results are presented, concerning a class of Banach spaces introduced by G. Godefroy and M. Talagrand, the representable Banach spaces. The main aspects considered here are the stability in forming tensor products, and the topological properties of the weak* dual unitball.

Radon Measures on Banach Spaces with their Weak Topologies

Jayne, J., Rogers, C. (1995)

Serdica Mathematical Journal

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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.