Operator space Lp embedding theory I

TL;DR

This paper introduces new free probability techniques to embed classical sequence spaces into the predual of large QWEP von Neumann algebras within the operator space framework.

Contribution

It provides the first construction of such embeddings for bcl_qb, expanding operator space embedding theory using free probability.

Findings

Successfully embeds bcl_qb into preduals of QWEP von Neumann algebras.

Develops new free probability methods for operator space embeddings.

Establishes isomorphic embeddings for all 1<qa0a0a02.

Abstract

Given any $1 < q \le 2$, we use new free probability techniques to construct a completely isomorphic embedding of $\ell_q$ (equipped with its natural operator space structure) into the predual of a sufficiently large QWEP von Neumann algebra.