Mathematische Annalen

, 335:109 | Cite as

Embedding of Cq and Rq into noncommutative Lp -spaces, 1≤p<q≤2

Article

Abstract

We prove that a quotient of a subspace of CppRp (1≤p<2) embeds completely isomorphically into a noncommutative Lp -space, where Cp and Rp are respectively the p-column and p-row Hilbertian operator spaces. We also represent Cq and Rq (p<q≤2) as quotients of subspaces of CppRp. Consequently, Cq and Rq embed completely isomorphically into a noncommutative Lp (M). We further show that the underlying von Neumann algebra M cannot be semifinite.

Mathematics subject classification (2000)

Primary 46L07 Secondary 47L25 

Keywords

embedding p-column and p-row spaces noncommutative Lp-spaces interpolation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon, cedexFrance

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