Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras

Research output: Contribution to journal › Journal article › Research › peer-review

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Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras. / Clouâtre, Raphaël; Dor-On, Adam.

In: International Mathematics Research Notices, Vol. 2024, No. 1, 2024, p. 698–744.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Clouâtre, R & Dor-On, A 2024, 'Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras', International Mathematics Research Notices, vol. 2024, no. 1, pp. 698–744. https://doi.org/10.1093/imrn/rnad062

APA

Clouâtre, R., & Dor-On, A. (2024). Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras. International Mathematics Research Notices, 2024(1), 698–744. https://doi.org/10.1093/imrn/rnad062

Vancouver

Clouâtre R, Dor-On A. Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras. International Mathematics Research Notices. 2024;2024(1):698–744. https://doi.org/10.1093/imrn/rnad062

Author

Clouâtre, Raphaël ; Dor-On, Adam. / Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras. In: International Mathematics Research Notices. 2024 ; Vol. 2024, No. 1. pp. 698–744.

Bibtex

@article{c1e0eba691a74277ad32a516bcb5c990,
title = "Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras",
abstract = "The residual finite-dimensionality of a C∗-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. While numerous subtleties emerge in this greater generality, we exhibit novel tools for constructing finite-dimensional approximations. One such tool is a notion of a residually finite-dimensional coaction of a semigroup on an operator algebra, which allows us to construct finite-dimensional approximations for operator algebras of functions and operator algebras of semigroups. Our investigation is intimately related to the question of when residual finite-dimensionality of an operator algebra is inherited by its maximal C∗-cover, which we establish in many cases of interest.",
author = "Rapha{\"e}l Clou{\^a}tre and Adam Dor-On",
note = "Publisher Copyright: {\textcopyright} 2023 The Author(s). Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.",
year = "2024",
doi = "10.1093/imrn/rnad062",
language = "English",
volume = "2024",
pages = "698–744",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras

AU - Clouâtre, Raphaël

AU - Dor-On, Adam

N1 - Publisher Copyright: © 2023 The Author(s). Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

PY - 2024

Y1 - 2024

N2 - The residual finite-dimensionality of a C∗-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. While numerous subtleties emerge in this greater generality, we exhibit novel tools for constructing finite-dimensional approximations. One such tool is a notion of a residually finite-dimensional coaction of a semigroup on an operator algebra, which allows us to construct finite-dimensional approximations for operator algebras of functions and operator algebras of semigroups. Our investigation is intimately related to the question of when residual finite-dimensionality of an operator algebra is inherited by its maximal C∗-cover, which we establish in many cases of interest.

AB - The residual finite-dimensionality of a C∗-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this paradigm to general (possibly non-self-adjoint) operator algebras. While numerous subtleties emerge in this greater generality, we exhibit novel tools for constructing finite-dimensional approximations. One such tool is a notion of a residually finite-dimensional coaction of a semigroup on an operator algebra, which allows us to construct finite-dimensional approximations for operator algebras of functions and operator algebras of semigroups. Our investigation is intimately related to the question of when residual finite-dimensionality of an operator algebra is inherited by its maximal C∗-cover, which we establish in many cases of interest.

U2 - 10.1093/imrn/rnad062

DO - 10.1093/imrn/rnad062

M3 - Journal article

AN - SCOPUS:85183161744

VL - 2024

SP - 698

EP - 744

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 1

ER -

ID: 382446825