Rosenthal's theorem for subspaces of noncommutative Lp

Details Rosenthal's theorem for subspaces of noncommutative Lp Rosenthal's theorem for subspaces of noncommutative Lp

2006-04-24

arxiv.org/abs/math/0604510v2

Mathematics

Functional Analysis

42 pages

Scientific paper

We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative Lp space for some p>1. This is a noncommutative version of Rosenthal's result for commutative Lp spaces. Similarly for 1 < q < 2, an infinite dimensional subspace X of a noncommutative Lq space either contains lq or embeds in Lp for some q < p < 2. The novelty in the noncommutative setting is a double sided change of density.

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