Spectrum of Class wF(p,r,q) Operators - Zongsheng Gao; Jiangtao Yuan (Journal of Inequalities and Applications, 2007)
This paper discusses some spectral properties of class wF(p,r,q) operators for p>0, r>0, p+rÃ¢Â‰Â¤1, and qÃ¢Â‰Â¥1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent EÃŽÂ» of T with respect to each nonzero isolated point spectrum ÃŽÂ» is selfadjoint and EÃŽÂ»Ã¢Â„Â‹=ker(TÃ¢ÂˆÂ’ÃŽÂ»)=ker(TÃ¢ÂˆÂ’ÃŽÂ»)Ã¢ÂˆÂ—. Afterwards, we prove that every class wF(p,r,q) operator has SVEP and property (ÃŽÂ²), and Weyl's theorem holds for f(T) when fÃ¢ÂˆÂˆH(ÃÂƒ(T)).