Spectral Properties of k-Quasi-M-hyponormal Operators

摘要

In this paper, we study the k-quasi-M-hyponormal operator and mainly prove that if T is a k-quasi-M-hyponormal operator, then sigma(ja)(T){0} = sigma(a)(T){0}, and the spectrum is continuous on the class of all k-quasi-M-hyponormal operators; let d(AB) is an element of B(B(H)) denote either the generalized derivation delta(AB) = L-A - R-B or the elementary operator Delta(AB) = L-A R-B - I, we show that if A and B* are k-quasi-M-hyponormal operators, then d(AB) is polaroid and generalized Weyl's theorem holds for f (d(AB)), where f is an analytic function on sigma(d(AB)) and f is not constant on each connected component of the open set U containing sigma(d(AB)). In additon, we discuss the hyperinvariant subspace problem for k-quasi-M-hyponormal operators.