The universal renorming
type: Item
instance of: scholarly article
title: The universal renorming
zbMATH Open document ID: 1319.46004
published in: Israel Journal of Mathematics
publication date: 2014-10-24T00:00:00Z
review text: The author introduces the universal renorming technique. It gives a formal way to determine any equivalent renorming of a real normed space. Using this tool, the author proves that every real normed space with property \(\alpha\) admits an equivalent renorming so that the set of non norm-attaining functionals is nowhere dense. In particular, this applies to the class of weakly compactly generated spaces. This is achieved by studying the algebraic and geometrical properties of the universal renorming and their relationship with strongly exposed points and smooth faces of the unit ball of the space.
reviewed by: Javier Merí
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B04
zbMATH DE Number: 6361341
zbMATH Keywords: universal renorming
zbMATH Keywords: non norm-attaining functional
zbMATH Keywords: exposed point
zbMATH Keywords: smooth face
author: Francisco García-Pacheco
MaRDI profile type: Publication
full work available at URL: s11856-014-1074-3
OpenAlex ID: W2032227161
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DOI: 10.1007/S11856-014-1074-3
description: scientific article; zbMATH DE number 6361341