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

  • Jonathan M. Borwein (a1) and Simon Fitzpatrick (a2)
Abstract

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.

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References
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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