Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Normal operators in $C^*$-algebras
without nice approximants

Authors: Don Hadwin and Terry A. Loring
Journal: Proc. Amer. Math. Soc. 125 (1997), 159-161
MSC (1991): Primary 46L80, 47A58; Secondary 46L05, 47C15
MathSciNet review: 1371125
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Abstract: The second author constructed a separable direct limit $C^*$-algebra with real rank zero containing a normal element whose spectrum is the closed unit disk that is not the limit of normal elements in the limiting algebras, and is not a limit of normals in the algebra having finite spectrum. We use Fredholm index theory to modify and simplify this construction to obtain such examples that are not limits of any ``nice'' types of elements.

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Additional Information

Don Hadwin
Affiliation: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824

Terry A. Loring
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131

Received by editor(s): July 3, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society