, Volume 335, Issue 1, pp 109-131
Date: 13 Mar 2006

Embedding of C q and R q into noncommutative L p -spaces, 1≤p<q≤2

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Abstract

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