Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 47A10

Retrieve articles in all journals with MSC (1991): 47A10

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

Woo Young Lee
Affiliation: Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea

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

American Mathematical Society