Normal operators in -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 -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

Email:
don@math.unh.edu

**Terry A. Loring**

Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131

Email:
loring@deepthought.unm.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03734-9

Received by editor(s):
July 3, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society