Operator space embedding of schatten p-classes into von Neumann algebra preduals

Marius Junge; Javier Parcet

doi:10.1007/s00039-008-0660-0

Operator space embedding of schatten p-classes into von Neumann algebra preduals

Marius Junge, Javier Parcet

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let X₁ and X₂ 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 L₁(A) with A a QWEP von Neumann algebra.

Original language	English (US)
Pages (from-to)	522-551
Number of pages	30
Journal	Geometric and Functional Analysis
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00039-008-0660-0
State	Published - Jul 2008

Keywords

Free random variable
Noncommutative Lp space
Operator space

ASJC Scopus subject areas

Analysis
Geometry and Topology

Online availability

10.1007/s00039-008-0660-0

Library availability

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title = "Operator space embedding of schatten p-classes into von Neumann algebra preduals",

abstract = "Let X1 and X2 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 L1(A) with A a QWEP von Neumann algebra.",

keywords = "Free random variable, Noncommutative Lp space, Operator space",

author = "Marius Junge and Javier Parcet",

note = "Funding Information: Keywords and phrases: Noncommutative Lp space, operator space, free random variable. AMS Mathematics Subject Classification: 46L07, 46L51, 46L52, 46L54. M.J. partially supported by the NSF DMS-0556120. J.P. partially supported by {\textquoteleft}Programa Ram{\'o}n y Cajal 2005{\textquoteright}, Spain; and partially supported by Grants MTM2007-60952 and CCG06-UAM/ESP-0286, Spain.",

year = "2008",

month = jul,

doi = "10.1007/s00039-008-0660-0",

language = "English (US)",

volume = "18",

pages = "522--551",

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publisher = "Birkhauser Verlag Basel",

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TY - JOUR

T1 - Operator space embedding of schatten p-classes into von Neumann algebra preduals

AU - Junge, Marius

AU - Parcet, Javier

N1 - Funding Information: Keywords and phrases: Noncommutative Lp space, operator space, free random variable. AMS Mathematics Subject Classification: 46L07, 46L51, 46L52, 46L54. M.J. partially supported by the NSF DMS-0556120. J.P. partially supported by ‘Programa Ramón y Cajal 2005’, Spain; and partially supported by Grants MTM2007-60952 and CCG06-UAM/ESP-0286, Spain.

PY - 2008/7

Y1 - 2008/7

N2 - Let X1 and X2 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 L1(A) with A a QWEP von Neumann algebra.

AB - Let X1 and X2 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 L1(A) with A a QWEP von Neumann algebra.

KW - Free random variable

KW - Noncommutative Lp space

KW - Operator space

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

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Operator space embedding of schatten p-classes into von Neumann algebra preduals

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