### Abstract

Let X_{1} and X_{2} be subspaces of quotients of R \oplus OH and C \oplus OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X1 ⊗h2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓ_q (equipped with its natural operator space structure) into L_{1}(A) with A a QWEP von Neumann algebra.

Original language | English (US) |
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Pages (from-to) | 522-551 |

Number of pages | 30 |

Journal | Geometric and Functional Analysis |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1 2008 |

### Keywords

- Free random variable
- Noncommutative Lp space
- Operator space

### ASJC Scopus subject areas

- Analysis
- Geometry and Topology

## Fingerprint Dive into the research topics of 'Operator space embedding of schatten p-classes into von Neumann algebra preduals'. Together they form a unique fingerprint.

## Cite this

Junge, M., & Parcet, J. (2008). Operator space embedding of schatten p-classes into von Neumann algebra preduals.

*Geometric and Functional Analysis*,*18*(2), 522-551. https://doi.org/10.1007/s00039-008-0660-0