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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

$ C\sp*$-algebras with Hausdorff spectrum


Authors: John W. Bunce and James A. Deddens
Journal: Trans. Amer. Math. Soc. 212 (1975), 199-217
MSC: Primary 46L05; Secondary 47C10
MathSciNet review: 0405116
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Abstract: By the spectrum of a $ {C^\ast}$-algebra we mean the set of unitary equivalence classes of irreducible representations equipped with the hull-kernel topology. We are concerned with characterizing the $ {C^\ast}$-algebras with identity which have Hausdorff spectrum. We characterize the $ {C^\ast}$-algebras with identity and bounded representation dimension which have Hausdorff spectrum. Our results are more natural when the $ {C^\ast}$-algebra is singly generated. For singly generated $ {C^\ast}$-algebras with unbounded representation dimension, we reduce the problem to the case when the generator is an infinite direct sum of irreducible finite scalar matrices, and we have partial results in this case.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0405116-1
Keywords: Hausdorff spectrum, GCR, bounded representation dimension, n-normal, pure n-normal, matrix units
Article copyright: © Copyright 1975 American Mathematical Society