Embedding of Cq and Rq into noncommutative Lp-spaces, 1 p<q 2
Quanhua Xu
Abstract
We prove that a quotient of 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<q2) 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.
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