Type II1 factors satisfying the spatial isomorphism conjecture.

Jan  Cameron; Erik Christensen; Allan M.  Sinclair; Roger R.  Smith; Stuart  White; Alan D.  Wiggins

Type II1 factors satisfying the spatial isomorphism conjecture.

Bidragets oversatte titel: Type II1 faktorer som opfylder den rumlige isomorfi hypotese.

Jan Cameron, Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart White, Alan D. Wiggins

Institut for Matematiske Fag

3 Citationer (Scopus)

Abstract

Det vises at hvis et par af von Neumann algebraer er tilstrækkeligt tæt på hinanden i Hausdorff-metrikken, og den ene er en II1 faktor, som er et krydset produkt af en abelsk von Neumann algebra med en gruuppvirkning af en gruppe men triviel begrænset kohomologi, så er de to algebraer unitært ækvivalente.

Bidragets oversatte titel	Type II1 faktorer som opfylder den rumlige isomorfi hypotese.
Originalsprog	Engelsk
Tidsskrift	Proceedings of the National Academy of Sciences USA (PNAS)
Vol/bind	109
Udgave nummer	5
Sider (fra-til)	20338 - 20343
Antal sider	6
ISSN	0027-8424
Status	Udgivet - 11 dec. 2012

Citationsformater

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title = "Type II1 factors satisfying the spatial isomorphism conjecture.",

abstract = "This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38-54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II1 factor with crossed products of abelian algebras by suitably chosen discrete groups.",

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year = "2012",

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language = "English",

volume = "109",

pages = "20338 -- 20343",

journal = "Proceedings of the National Academy of Sciences USA (PNAS)",

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TY - JOUR

T1 - Type II1 factors satisfying the spatial isomorphism conjecture.

AU - Cameron, Jan

AU - Christensen, Erik

AU - Sinclair, Allan M.

AU - Smith, Roger R.

AU - White, Stuart

AU - Wiggins, Alan D.

PY - 2012/12/11

Y1 - 2012/12/11

N2 - This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38-54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II1 factor with crossed products of abelian algebras by suitably chosen discrete groups.

AB - This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38-54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II1 factor with crossed products of abelian algebras by suitably chosen discrete groups.

M3 - Journal article

SN - 0027-8424

VL - 109

SP - 20338

EP - 20343

JO - Proceedings of the National Academy of Sciences USA (PNAS)

JF - Proceedings of the National Academy of Sciences USA (PNAS)

IS - 5

ER -

Type II1 factors satisfying the spatial isomorphism conjecture.

Abstract

Fingeraftryk

Citationsformater