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On commutative, operator amenable subalgebras of finite von Neumann algebras

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On commutative, operator amenable subalgebras of finite von Neumann algebras. / Choi, Yemon.
In: Journal für die reine und angewandte Mathematik (Crelle's Journal), Vol. 678, 05.2013, p. 201-222.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Choi, Y 2013, 'On commutative, operator amenable subalgebras of finite von Neumann algebras', Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 678, pp. 201-222. https://doi.org/10.1515/crelle.2012.030

APA

Choi, Y. (2013). On commutative, operator amenable subalgebras of finite von Neumann algebras. Journal für die reine und angewandte Mathematik (Crelle's Journal), 678, 201-222. https://doi.org/10.1515/crelle.2012.030

Vancouver

Choi Y. On commutative, operator amenable subalgebras of finite von Neumann algebras. Journal für die reine und angewandte Mathematik (Crelle's Journal). 2013 May;678:201-222. Epub 2012 Feb 23. doi: 10.1515/crelle.2012.030

Author

Choi, Yemon. / On commutative, operator amenable subalgebras of finite von Neumann algebras. In: Journal für die reine und angewandte Mathematik (Crelle's Journal). 2013 ; Vol. 678. pp. 201-222.

Bibtex

@article{f70175da2d6c4e69ba618a3744b6036e,
title = "On commutative, operator amenable subalgebras of finite von Neumann algebras",
abstract = "It has been conjectured, motivated in part by old results of Dixmier and Day on bounded Hilbertian representations of amenable groups, that every norm-closed amenable subalgebra of ℬ(ℋ) is automatically similar to an amenable C*-algebra. Results of Curtis and Loy (1995), Gifford (2006), and Marcoux (2008) give some evidence to support this conjecture, but it remains open even for commutative subalgebras.We present more evidence to support this conjecture, by showing that a closed, commutative, operator amenable subalgebra of a finite von Neumann algebra ℳ must be similar to a selfadjoint-subalgebra. Technical results used include an approximation argument based on Grothendieck's inequality and the Pietsch Domination Theorem, together with an adaptation of a theorem of Gifford to the setting of unbounded operators affiliated to ℳ.",
author = "Yemon Choi",
year = "2013",
month = may,
doi = "10.1515/crelle.2012.030",
language = "English",
volume = "678",
pages = "201--222",
journal = "Journal f{\"u}r die reine und angewandte Mathematik (Crelle's Journal)",
issn = "0075-4102",
publisher = "Walter de Gruyter GmbH & Co. KG",

}

RIS

TY - JOUR

T1 - On commutative, operator amenable subalgebras of finite von Neumann algebras

AU - Choi, Yemon

PY - 2013/5

Y1 - 2013/5

N2 - It has been conjectured, motivated in part by old results of Dixmier and Day on bounded Hilbertian representations of amenable groups, that every norm-closed amenable subalgebra of ℬ(ℋ) is automatically similar to an amenable C*-algebra. Results of Curtis and Loy (1995), Gifford (2006), and Marcoux (2008) give some evidence to support this conjecture, but it remains open even for commutative subalgebras.We present more evidence to support this conjecture, by showing that a closed, commutative, operator amenable subalgebra of a finite von Neumann algebra ℳ must be similar to a selfadjoint-subalgebra. Technical results used include an approximation argument based on Grothendieck's inequality and the Pietsch Domination Theorem, together with an adaptation of a theorem of Gifford to the setting of unbounded operators affiliated to ℳ.

AB - It has been conjectured, motivated in part by old results of Dixmier and Day on bounded Hilbertian representations of amenable groups, that every norm-closed amenable subalgebra of ℬ(ℋ) is automatically similar to an amenable C*-algebra. Results of Curtis and Loy (1995), Gifford (2006), and Marcoux (2008) give some evidence to support this conjecture, but it remains open even for commutative subalgebras.We present more evidence to support this conjecture, by showing that a closed, commutative, operator amenable subalgebra of a finite von Neumann algebra ℳ must be similar to a selfadjoint-subalgebra. Technical results used include an approximation argument based on Grothendieck's inequality and the Pietsch Domination Theorem, together with an adaptation of a theorem of Gifford to the setting of unbounded operators affiliated to ℳ.

U2 - 10.1515/crelle.2012.030

DO - 10.1515/crelle.2012.030

M3 - Journal article

VL - 678

SP - 201

EP - 222

JO - Journal für die reine und angewandte Mathematik (Crelle's Journal)

JF - Journal für die reine und angewandte Mathematik (Crelle's Journal)

SN - 0075-4102

ER -