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

Jiangtao Yuan and Zongsheng Gao

 LMIB and Department of Mathematics, Beihang University, Beijing 100083, China
Received 23 November 2006; Accepted 16 May 2007

Recommended by Jozsef Szabados

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

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)).