Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 27195, 10 pages
Research Article

Spectrum of Class wF(p,r,q) Operators

Jiangtao Yuan and Zongsheng Gao

LMIB and Department of Mathematics, Beihang University, Beijing 100083, China

Received 23 November 2006; Accepted 16 May 2007

Academic Editor: Jozsef Szabados

Dedicated to Professor Daoxing Xia on his 77th birthday with respect and affection

Copyright © 2007 Jiangtao Yuan and Zongsheng Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper discusses some spectral properties of class wF(p,r,q) operators for p>0, r>0, p+r1, and q1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent Eλ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and Eλ=ker(Tλ)=ker(Tλ). Afterwards, we prove that every class wF(p,r,q) operator has SVEP and property (β), and Weyl's theorem holds for f(T) when fH(σ(T)).