This is an announcement for the paper "Embedding of $C_q$ and $R_q$ into noncommutative $L_p$-spaces, $1\le p<q\le 2$" by Quanhua Xu.

Abstract: We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) 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 $R_q$ ($p<q\le2$) as quotients of subspaces of $C_p\oplus_pR_p$. 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.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: Primary 46L07; Secondary 47L25

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Submitted from: qx@math.univ-fcomte.fr

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