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Another note on Weyl's theorem
Author(s):
Robin
Harte;
Woo
Young
Lee
Journal:
Trans. Amer. Math. Soc.
349
(1997),
2115-2124.
MSC (1991):
Primary 47A10
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Abstract:
``Weyl's theorem holds" for an operator  on a Banach space  when the complement in the spectrum of the ``Weyl spectrum" coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the ``Browder spectrum", which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in  . In this note we try to explore these distinctions.
References:
- 1.
- S.K. Berberian, An extension of Weyl's theorem to a class of not necessarily normal operators, Michigan Math. Jour. 16 (1969), 273-279. MR 40:3335
- 2.
- S.K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. Jour. 20 (1970), 529-544. MR 43:5344
- 3.
- L.A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. Jour. 13 (1966), 285-288. MR 30:1846
- 4.
- R.E. Harte, Fredholm, Weyl and Browder theory, Proc. Royal Irish Acad. 85A (1985), 151-176. MR 87h:47029
- 5.
- R.E. Harte, Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), 328-330. MR 88d:46088
- 6.
- R.E. Harte, Invertibility and singularity for bounded linear operators, Dekker, New York, 1988. MR 89d:47001
- 7.
- W.Y. Lee and H.Y. Lee, On Weyl's theorem, Math. Japon. 39 (1994), 545-548. MR 95a:47008
- 8.
- W.Y. Lee and S.H. Lee, A spectral mapping theorem for the Weyl spectrum, Glasgow Math. Jour. 38 (1996), 61-64. CMP 1996:8
- 9.
- K.K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212. MR 48:12086
- 10.
- K.K. Oberai, On the Weyl spectrum II, Illinois J. Math. 21 (1977), 84-90. MR 55:1102
- 11.
- C.M. Pearcy, Some recent developements in operator theory, CBMS Regional Conf. Ser. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1978. MR 58:7120
- 12.
- J.G. Stampfli, Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117 (1965), 469-476. MR 33:4686
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Additional Information:
Robin
Harte
Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland
Address at time of publication:
Instituto de Mathematicas, Area de Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, Mexico DF, CP 04510
Email:
rharte@gauss.matem.unam.mx
Woo
Young
Lee
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea
Email:
wylee@yurim.skku.ac.kr
DOI:
10.1090/S0002-9947-97-01881-3
PII:
S 0002-9947(97)01881-3
Keywords:
Weyl's theorem,
Browder's theorem,
Riesz points
Received by editor(s):
December 18, 1995
Additional Notes:
The second author was supported in part by BSRI-95-1420 and KOSEF (94-0701-02-01-3, GARC)
Copyright of article:
Copyright
1997,
American Mathematical Society
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