Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type

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Standard

Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type. / Ando, Hiroshi; Matsuzawa, Yasumichi; Thom, Andreas; Törnquist, Asger Dag.

I: Journal fuer die Reine und Angewandte Mathematik, Bind 758, 2020, s. 223-251.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Ando, H, Matsuzawa, Y, Thom, A & Törnquist, AD 2020, 'Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type', Journal fuer die Reine und Angewandte Mathematik, bind 758, s. 223-251. https://doi.org/10.1515/crelle-2017-0047

APA

Ando, H., Matsuzawa, Y., Thom, A., & Törnquist, A. D. (2020). Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type. Journal fuer die Reine und Angewandte Mathematik, 758, 223-251. https://doi.org/10.1515/crelle-2017-0047

Vancouver

Ando H, Matsuzawa Y, Thom A, Törnquist AD. Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type. Journal fuer die Reine und Angewandte Mathematik. 2020;758:223-251. https://doi.org/10.1515/crelle-2017-0047

Author

Ando, Hiroshi ; Matsuzawa, Yasumichi ; Thom, Andreas ; Törnquist, Asger Dag. / Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type. I: Journal fuer die Reine und Angewandte Mathematik. 2020 ; Bind 758. s. 223-251.

Bibtex

@article{16635753383f461ba27ae26701dd5eb4,
title = "Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type",
abstract = "Let Γ be a countable discrete group, and let π:Γ→GL(H) be a representation of Γ by invertible operators on a separable Hilbert space H. We show that the semidirect product group G=H⋊πΓ is SIN (G admits a two-sided invariant metric compatible with its topology) and unitarily representable (G embeds into the unitary group U(ℓ2(N))) if and only if π is uniformly bounded, and that π is unitarizable if and only if G is of finite type, that is, G embeds into the unitary group of a II1-factor. Consequently, we show that a unitarily representable Polish SIN group need not be of finite type, answering a question of Sorin Popa. The key point in our argument is an equivariant version of the Maurey–Nikishin factorization theorem for continuous maps from a Hilbert space to the space L0(X,m) of all measurable maps on a probability space.",
author = "Hiroshi Ando and Yasumichi Matsuzawa and Andreas Thom and T{\"o}rnquist, {Asger Dag}",
year = "2020",
doi = "10.1515/crelle-2017-0047",
language = "English",
volume = "758",
pages = "223--251",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",

}

RIS

TY - JOUR

T1 - Unitarizability, Maurey-Nikishin factorization, and Polish groups of finite type

AU - Ando, Hiroshi

AU - Matsuzawa, Yasumichi

AU - Thom, Andreas

AU - Törnquist, Asger Dag

PY - 2020

Y1 - 2020

N2 - Let Γ be a countable discrete group, and let π:Γ→GL(H) be a representation of Γ by invertible operators on a separable Hilbert space H. We show that the semidirect product group G=H⋊πΓ is SIN (G admits a two-sided invariant metric compatible with its topology) and unitarily representable (G embeds into the unitary group U(ℓ2(N))) if and only if π is uniformly bounded, and that π is unitarizable if and only if G is of finite type, that is, G embeds into the unitary group of a II1-factor. Consequently, we show that a unitarily representable Polish SIN group need not be of finite type, answering a question of Sorin Popa. The key point in our argument is an equivariant version of the Maurey–Nikishin factorization theorem for continuous maps from a Hilbert space to the space L0(X,m) of all measurable maps on a probability space.

AB - Let Γ be a countable discrete group, and let π:Γ→GL(H) be a representation of Γ by invertible operators on a separable Hilbert space H. We show that the semidirect product group G=H⋊πΓ is SIN (G admits a two-sided invariant metric compatible with its topology) and unitarily representable (G embeds into the unitary group U(ℓ2(N))) if and only if π is uniformly bounded, and that π is unitarizable if and only if G is of finite type, that is, G embeds into the unitary group of a II1-factor. Consequently, we show that a unitarily representable Polish SIN group need not be of finite type, answering a question of Sorin Popa. The key point in our argument is an equivariant version of the Maurey–Nikishin factorization theorem for continuous maps from a Hilbert space to the space L0(X,m) of all measurable maps on a probability space.

UR - http://www.scopus.com/inward/record.url?scp=85037690404&partnerID=8YFLogxK

U2 - 10.1515/crelle-2017-0047

DO - 10.1515/crelle-2017-0047

M3 - Journal article

VL - 758

SP - 223

EP - 251

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

ER -

ID: 184033442