Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
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
APA
Vancouver
Author
Bibtex
}
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