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A Weak Hadamard Smooth Renorming of L 1(Ω, μ)

Published online by Cambridge University Press:  20 November 2018

Jonathan M. Borwein  and
Simon Fitzpatrick
Jonathan M. Borwein
Affiliation:
Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1
Simon Fitzpatrick
Affiliation:
Department of Mathematics University of Western Australia Nedlands, W.A. 6019 Australia
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Abstract

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We show that L 1(μ) has a weak Hadamard differential)le renorm (i.e. differentiable away from the origin uniformly on all weakly compact sets) if and only if μ is sigma finite. As a consequence several powerful recent differentiability theorems apply to subspaces of L 1.

Keywords

46A1746B2246B0346B15Asplund spacesMackey convergenceweak Hadamard derivativesrenormsDunford-Pettis propertylocally Mackey rotundbornological derivatives

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 4 , 01 December 1993 , pp. 407 - 413
Copyright
Copyright © Canadian Mathematical Society 1993

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