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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1407492
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Abstract: ``Weyl's theorem holds" for an operator $T$ on a Banach space $X$ 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 $T$. 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: http://dx.doi.org/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)
Article copyright: © Copyright 1997 American Mathematical Society