Israel Journal of Mathematics

, Volume 163, Issue 1, pp 1–27

Embeddings of non-commutative Lp-spaces into preduals of finite von Neumann algebras

Article

DOI: 10.1007/s11856-008-0001-x

Cite this article as:
Randrianantoanina, N. Isr. J. Math. (2008) 163: 1. doi:10.1007/s11856-008-0001-x

Abstract

Let \(\mathcal{R}\) be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra \(\mathcal{N}\) so that for every 1 < p < 2, the Haagerup Lp-space associated with \(\mathcal{R}\) embeds isomorphically into \(\mathcal{N}_ * \). We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if \(\mathcal{M}\) is a semi-finite von Neumann algebra then every reflexive subspace of \(\mathcal{M}_ * \) embeds isomorphically into Lr (\(\mathcal{M}\)) for some r > 1.

Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMiami UniversityOxfordUSA

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