Finite dimensional subspaces of noncommutative $L_p$ spaces

Abstract

We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \leq c_p n^{\abs{1/2-1/p}} for some constant c_p depending only on $p$, where $1/p+1/p^{\prime }=1$ and $R{C}_{p^{\prime }}^n=[R_n\cap C_n,R_n+C_n{]}_{1/p^{\prime }}$. Moreover, there is a projection $P:Lp(M)-->Lp(M)$ onto E with $\norm{P}_{cb} \leq c_p n^{\abs{1/2-1/p}}.$ We follow the classical change of density argument with appropriate noncommutative variations in addition to the opposite trick.

This paper has been withdrawn due to a crucial error in the proof of Proposition 3.2

References in corpus (5)

• Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps
• On the maximality of subdiagonal algebras
• Type and cotype of operator spaces
• Tsirelson like operator spaces
• Rosenthal's theorem for subspaces of noncommutative Lp