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CENTRAL SEQUENCES IN SUBHOMOGENEOUS UNITAL C*-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  02 October 2020

DON HADWIN  and
HEMANT PENDHARKAR
DON HADWIN
Affiliation:
Mathematics Department, University of New Hampshire, Durham, New Hampshire, USA e-mail: don@unh.edu
HEMANT PENDHARKAR*
Affiliation:
Department of Mathematics and Statistics, University of South Florida, Tampa, Florida, USA
*
e-mail: pendharkar@usf.edu
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Abstract

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Suppose that $\mathcal {A}$ is a unital subhomogeneous C*-algebra. We show that every central sequence in $\mathcal {A}$ is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in $\mathcal {A}$ is trivial if and only if every pointwise limit of irreducible representations is irreducible. Finally, we give a nice representation of the latter algebras.

Keywords

central sequencehypercentral sequencesubhomogeneousC*-algebra

MSC classification

Primary: 46L40: Automorphisms
Secondary: 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 2 , April 2021 , pp. 318 - 325
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

References

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