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

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

MathSciNet review:
1371125

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Abstract | References | Similar Articles | Additional Information

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.

**1.**L. G. Brown, R. G. Douglas and P.A. Fillmore,*Unitary equivalence modulo the compact operators and extensions of -algebras*, Lecture Notes in Math., vol. 345, Springer-Verlag, New York, 1973. MR**52:1378****2.**J. B. Conway,*The theory of subnormal operators*, Math. Surveys and Monographs, vol. 36, Amer. Math. Soc., Providence, RI, 1991. MR**92h:47026****3.**K. F. Clancy,*Seminormal operators*, Lecture Notes in Math., vol. 742, Springer-Verlag, New York, 1979.**4.**D. Hadwin,*Strongly quasidiagonal -algebras*, J. Operator Th.**18**(1987), 3-18. MR**89d:46060****5.**T. Loring,*Normal elements of -algebras of real rank zero without finite-spectrum approximants*, J. London Math. Soc. (2)**51**(1995), 353-364. MR**96b:46099****6.**T. Loring and J. Spielberg,*Approximation of normal elements in the multiplier algebra of an AF -algebra*, Proc. Amer. Math. Soc.**12**(1994), 1173-1175. MR**94k:46116**

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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