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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the Kyung Hee University Research Fund in 2007 (KHU- 20071605).
Rights and permissions
About this article
Cite this article
An, I.J., Han, Y.M. Weyl’s Theorem for Algebraically Quasi-class A Operators. Integr. equ. oper. theory 62, 1–10 (2008). https://doi.org/10.1007/s00020-008-1599-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00020-008-1599-0