Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras

Raphaël Clouâtre, Adam Dor-On

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)22138-22184
Number of pages47
JournalInternational Mathematics Research Notices
Volume2023
Issue number24
DOIs
StatePublished - 1 Dec 2023
Externally publishedYes

Bibliographical note

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

ASJC Scopus subject areas

  • General Mathematics

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