The Properties of κ-quasi-*-A(n) Operator

摘要

An operator T is called k-quasi-*-A(n) operator,if T*k|T1+n|2/1+nTk ≥T*k|T*|2Tk,k ∈ Z,which is a generalization of quasi-*-A(n) operator.In this paper we prove some properties of k-quasi-*-A(n) operator,such as,if T is a k-quasi-*-A(n) operator and N(T) (∈)N(T*),then its point spectrum and joint point spectrum are identical.Using these results,we also prove that if T is a k-quasi-*-A(n) operator and N(T) (∈) N(T*),then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.