Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 27195, 10 pages
doi:10.1155/2007/27195
Research Article
Spectrum of Class wF(p,r,q) Operators
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.
Abstract
This paper discusses some spectral properties of class wF(p,r,q) operators for p>0, r>0, p+r≤1, and q≥1. 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 Eλℋ=ker(T−λ)=ker(T−λ)∗. 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 f∈H(σ(T)).