Geodesic
A Weak Hadamard Smooth Renorming of L 1(Ω, μ)
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 407-413

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DOI

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.
DOI : 10.4153/CMB-1993-055-5
Mots-clés : 46A17, 46B22, 46B03, 46B15, Asplund spaces, Mackey convergence, weak Hadamard derivatives, renorms, Dunford-Pettis property, locally Mackey rotund, bornological derivatives 
Borwein, Jonathan M.; Fitzpatrick, Simon. A Weak Hadamard Smooth Renorming of L 1(Ω, μ). Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 407-413. doi: 10.4153/CMB-1993-055-5
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     journal = {Canadian mathematical bulletin},
     pages = {407--413},
     year = {1993},
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     doi = {10.4153/CMB-1993-055-5},
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