Finite-Dimensional Approximations and Semigroup Coactions for Operator Algebras
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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.
Originalsprog | Engelsk |
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Tidsskrift | International Mathematics Research Notices |
Vol/bind | 2024 |
Udgave nummer | 1 |
Sider (fra-til) | 698–744 |
ISSN | 1073-7928 |
DOI | |
Status | Udgivet - 2024 |
Bibliografisk note
Funding Information:
This work was partially supported by an NSERC Discovery grant [RGPIN-2022-03600 to R.C.]; the NSF [DMS-1900916 to A.D.-O.]; and the European Union’s Horizon 2020 Marie Skłodowska-Curie [839412 to A.D.-O.].
Publisher Copyright:
© 2023 The Author(s). Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.
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