A Weak Hadamard Smooth Renorming of <i>L</i><sub>1</sub>(Ω, <i>μ</i>)
A Weak Hadamard Smooth Renorming of <i>L</i><sub>1</sub>(Ω, <i>μ</i>)
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 .