Another note on Weyl's theorem

Authors:
Robin Harte and Woo Young Lee

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2115-2124

MSC (1991):
Primary 47A10

DOI:
https://doi.org/10.1090/S0002-9947-97-01881-3

MathSciNet review:
1407492

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9947-97-01881-3

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)

Article copyright:
© Copyright 1997
American Mathematical Society