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Locally uniformly rotund norms

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

M. Raja
M. Raja
Affiliation:
Mathçmatiques Pures, Universitç Bordeaux 1351, cours de la Liberation, 33405 Talance Cedex, France. E-mail: matias@um.es
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Abstract

Given a Banach space X and a norming subspace Z⊂X*, a geometrical method is introduced to characterize the existence of an equivalent σ(X, Z)-lsc LUR norm on X. A new simple proof of the Theorem of Troyanski: every rotund space with a Kadec norm is LUR renormable, and a generalization of the Moltó, Orihuela and Troyanski characterization of the LUR renormability, are provided without probability arguments. Among other applications, it is shown that a dual Banach space with a w*-Kadec norm admits a dual LUR norm.

MSC classification

Secondary: 46B07: Local theory of Banach spaces
Type
Research Article
Information
Mathematika , Volume 46 , Issue 2 , December 1999 , pp. 343 - 358
Copyright
Copyright © University College London 1999

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