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Integral Equations and Operator Theory

, Volume 62, Issue 1, pp 1–10 | Cite as

Weyl’s Theorem for Algebraically Quasi-class A Operators

  • Il Ju An
  • Young Min HanEmail author
Article

Abstract.

If T or T* is an algebraically quasi-class A operator acting on an infinite dimensional separable Hilbert space then we prove that Weyl’s theorem holds for f(T) for every f H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is algebraically quasi-class A then a-Weyl’s theorem holds for f(T). Also, if T or T* is an algebraically quasi-class A operator then we establish that the spectral mapping theorems for the Weyl spectrum and the essential approximate point spectrum of T for every f H(σ(T)), respectively.

Keywords.

Weyl’s theorem Browder’s theorem algebraically quasi-class A operator a-Weyl’s theorem a-Browder’s theorem single valued extension property 

Mathematics Subject Classification (2000).

Primary 47A10, 47A53 Secondary 47B20 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Research Institute for Basic SciencesKyung Hee UniversitySeoulKorea

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