Boundaries of a convex set and interpolation sets
type: Item
instance of: scholarly article
title: Boundaries of a convex set and interpolation sets
zbMATH Open document ID: 0597.46015
DOI: 10.1007/BF01457357
author: Gilles Godefroy
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164243
review text: We study the boundary structure of norm-closed and \(w^*\)-closed convex sets, in connection with R. C. James's techniques, H. P. Rosenthal's theorem, and interpolation sets in harmonic analysis. We improve some results of J. F. Méla, E. Saab and H. P. Rosenthal. We show that an equivalent norm on the dual of a separable space not containing \(\ell^ 1({\mathbb{N}})\) is dual if and only if all the \(w^*\)-closed hyperplanes are proximinal. If E is weakly \({\mathfrak K}\)-analytic - e.g. separable - then a norming subspace X of \(E^*\) is an isometric predual of E if and only if every element of X attains its norm; it is also true if \(X^{**}\) is the \(w^*\)-sequential closure of X. We give examples which show that those results are sharp.
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 3962463
zbMATH Keywords: boundary structure of norm-closed and \(w^ *\)-closed convex sets
zbMATH Keywords: interpolation sets
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3962463