Rosenthal's theorem for subspaces of noncommutative Lp
Functional Analysis
2007-05-23 v2 Operator Algebras
Abstract
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.
Cite
@article{arxiv.math/0604510,
title = {Rosenthal's theorem for subspaces of noncommutative Lp},
author = {Marius Junge and Javier Parcet},
journal= {arXiv preprint arXiv:math/0604510},
year = {2007}
}
Comments
42 pages