Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-13T20:57:37.635Z Has data issue: false hasContentIssue false
  • English
  • Français

A spectral mapping theorem for the Weyl spectrum

Published online by Cambridge University Press:  18 May 2009

Woo Young Lee and
Sang Hoon Lee
Woo Young Lee
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea, E-mail address: wylee@yurim.skku.ac.kr
Sang Hoon Lee
Affiliation:
Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea, E-mail address: wylee@yurim.skku.ac.kr
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Suppose H is a Hilbert space and write ℒ(H) for the set of all bounded linear operators on H. If T ∈ ℒ(H) we write σ(T) for the spectrum of T; π0(T) for the set of eigenvalues of T; and π00(T) for the isolated points of σ(T) that are eigenvalues of finite multiplicity. If K is a subset of C, we write iso K for the set of isolated points of K. An operator T ∈ ℒ(H) is said to be Fredholm if both T−1(0) and T(H)⊥ are finite dimensional. The index of a Fredholm operator T, denoted by index(T), is defined by

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 38 , Issue 1 , January 1996, pp. 61 - 64
Copyright
Copyright © Glasgow Mathematical Journal Trust 1996

References

REFERENCES

1.Berberian, S. K., An extension of Weyl's theorem to a class of not necessary normal operators, Michigan Math. J. 16 (1969), 273–279.CrossRefGoogle Scholar
2.Berberian, S. K., The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970, 1971), 529–544.CrossRefGoogle Scholar
3.Conway, J. B., Subnormal operators (Pitman, Boston, 1981).Google Scholar
4.Coburn, L. A., Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288.CrossRefGoogle Scholar
5.Gramsch, G. and Lay, D., Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17–32.CrossRefGoogle Scholar
6.Halmos, P. R., A Hilbert space problem book (Springer-Verlag, 1984).Google Scholar
7.Harte, R. E., Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. Sect. A. 85 (1985), 151–176.Google Scholar
8.Harte, R. E., Invertibility and singularity for bounded linear operators (Marcel Dekker, 1988).Google Scholar
9.Lee, W. Y. and Lee, H. Y., On Weyl's theorem, Math. Japon 39 (1994), 545–548.Google Scholar
10.Oberai, K. K., On the Weyl spectrum, Illinois J. Math. 18 (1974), 208–212.CrossRefGoogle Scholar
11.Oberai, K. K., On the Weyl spectrum (II), Illinois J. Math. 21 (1977), 84–90.CrossRefGoogle Scholar
12.Stampfli, J. G., Hyponormal operators, Pacific J. Math. 12 (1962), 1453–1458.CrossRefGoogle Scholar