Moduli of convexity and smoothness of reflexive subspaces of L^1

Details Moduli of convexity and smoothness of reflexive subspaces of L^1 Moduli of convexity and smoothness of reflexive subspaces of L^1

2011-04-14

arxiv.org/abs/1104.2802v1

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jfa.2011.07.024

We show that for any probability measure \mu there exists an equivalent norm
on the space L^1(\mu) whose restriction to each reflexive subspace is uniformly
smooth and uniformly convex, with modulus of convexity of power type 2. This
renorming provides also an estimate for the corresponding modulus of smoothness
of such subspaces.

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