tailieunhanh - Báo cáo hóa học: " Research Article Spectrum of Class wF(p,r, q) Operators Jiangtao Yuan and Zongsheng Gao"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Spectrum of Class wF(p,r, q) Operators Jiangtao Yuan and Zongsheng Gao | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID27195 10 pages doi 2007 27195 Research Article Spectrum of Class wF p r q Operators Jiangtao Yuan and Zongsheng Gao Received 23 November 2006 Accepted 16 May 2007 Dedicated to Professor Daoxing Xia on his 77th birthday with respect and affection Recommended by Jozsef Szabados 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 Ea of T with respect to each nonzero isolated point spectrum A is selfadjoint and EÀX. ker T - A ker T - A . Afterwards we prove that every class wF p r q operator has SVEP and property P and Weyl s theorem holds for f T when f e H ơ T . Copyright 2007 J. Yuan and Z. 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. 1. Introduction A capital letter such as T means a bounded linear operator on a complex Hilbert space GX. For p 0 an operator T is said to be p-hyponormal if T T p TT p where T is the adjoint operator of T. An invertible operator T is said to be log-hyponormal if log T T log TT . If p 1 T is called hyponormal and if p 1 2 T is called semihyponormal. Log-hyponormality is sometimes regarded as 0-hyponormal since Xp -1 p logX as p 0 for X 0. See Martin and Putinar 1 and Xia 2 for basic properties of hyponormal and semihyponormal operators. Log-hyponormal operators were introduced by Tanahashi 3 Aluthge and Wang 4 and Fujii et al. 5 independently. Aluthge 6 introduced p-hyponormal operators. As generalizations of p-hyponormal and log-hyponormal operators many authors introduced many classes of operators. Aluthge and Wang 4 introduced w-hyponormal operators defined by T ITI I T I where the polar decomposition of T is T UITI and T IT11 2 UIT11 2 is .