Normal operators in algebras without nice approximants
Authors:
Don Hadwin and Terry A. Loring
Journal:
Proc. Amer. Math. Soc. 125 (1997), 159161
MSC (1991):
Primary 46L80, 47A58; Secondary 46L05, 47C15
MathSciNet review:
1371125
Fulltext PDF Free Access
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 𝐶*algebras, Proceedings of a Conference on
Operator Theory (Dalhousie Univ., Halifax, N.S., 1973), Springer, Berlin,
1973, pp. 58–128. Lecture Notes in Math., Vol. 345. MR 0380478
(52 #1378)
 2.
John
B. Conway, The theory of subnormal operators, Mathematical
Surveys and Monographs, vol. 36, American Mathematical Society,
Providence, RI, 1991. MR 1112128
(92h:47026)
 3.
K. F. Clancy, Seminormal operators, Lecture Notes in Math., vol. 742, SpringerVerlag, New York, 1979.
 4.
Don
Hadwin, Strongly quasidiagonal 𝐶*algebras, J.
Operator Theory 18 (1987), no. 1, 3–18. With an
appendix by Jonathan Rosenberg. MR 912809
(89d:46060)
 5.
Terry
A. Loring, Normal elements of 𝐶*algebras of real rank zero
without finitespectrum approximants, J. London Math. Soc. (2)
51 (1995), no. 2, 353–364. MR 1325578
(96b:46099), http://dx.doi.org/10.1112/jlms/51.2.353
 6.
Terry
A. Loring and Jack
Spielberg, Approximation of normal elements in
the multiplier algebra of an AF 𝐶*algebra, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1173–1175. MR 1211584
(94k:46116), http://dx.doi.org/10.1090/S00029939199412115845
 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, SpringerVerlag, 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, SpringerVerlag, New York, 1979.
 4.
 D. Hadwin, Strongly quasidiagonal algebras, J. Operator Th. 18 (1987), 318. MR 89d:46060
 5.
 T. Loring, Normal elements of algebras of real rank zero without finitespectrum approximants, J. London Math. Soc. (2) 51 (1995), 353364. 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), 11731175. MR 94k:46116
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (1991):
46L80,
47A58,
46L05,
47C15
Retrieve articles in all journals
with MSC (1991):
46L80,
47A58,
46L05,
47C15
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:
http://dx.doi.org/10.1090/S0002993997037349
PII:
S 00029939(97)037349
Received by editor(s):
July 3, 1995
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997 American Mathematical Society
