Displaying similar documents to “Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces”

Some Applications of Simons’ Inequality

Godefroy, Gilles (2000)

Serdica Mathematical Journal

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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

Frontisi, Julien (1996)

Serdica Mathematical Journal

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It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

G. Androulakis (1998)

Studia Mathematica

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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...