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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

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.

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References

Akemann, C. A. and Pedersen, G. K., ‘Central sequences and inner derivations of separable C*-algebras’, Amer. J. Math. 101(5) (1979), 1047–1061.CrossRefGoogle Scholar
Ando, H. and Kirchberg, E., ‘Non-commutativity of the central sequence algebra for separable non-type I C*-algebras’, J. Lond. Math. Soc. (2) 94(1) (2016), 280–294.CrossRefGoogle Scholar
Glimm, J., ‘A Stone–Weierstrass theorem for C*-algebras’, Ann. of Math. (2) 72 (1960), 216–244.CrossRefGoogle Scholar
McDuff, D., ‘Central sequences and the hyperfinite factor’, Proc. Lond. Math. Soc. (3) 21 (1970), 443–461.CrossRefGoogle Scholar
Pendharkar, H., Central Sequences and C*-Algebras, PhD Dissertation, University of New Hampshire, 1999.Google Scholar
Phillips, J., ‘Central sequences and automorphisms of C*-algebras’, Amer. J. Math. 110(6) (1988), 1095–1117.CrossRefGoogle Scholar
Robert, L., ‘Is there an upper bound on the dimension for irreducible representations of a continuous trace C*-algebra?’ Mathoverflow, https://mathoverflow.net/q/110582 (version: 2012-10-26).Google Scholar