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Embedding of $C_q$ and $R_q$ into noncommutative $L_p$-spaces, $1\le p<q\le 2$

Quanhua Xu
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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.

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Quanhua Xu. 2005-05-14. Embedding of $C_q$ and $R_q$ into noncommutative $L_p$-spaces, $1\le p<q\le 2$. https://arxiv.org/abs/math/0505307

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