Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Don Hadwin; 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.

References:

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