English

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.

Keywords

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

R2 v1 2026-07-22T17:34:53.746Z