Article

Israel Journal of Mathematics

, Volume 163, Issue 1, pp 1-27

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

  • Narcisse RandrianantoaninaAffiliated withDepartment of Mathematics and Statistics, Miami University Email author 

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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 L p -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 L r (\(\mathcal{M}\)) for some r > 1.