On quasi-M-hyponormal operators

Abstract

An operator T is called quasi-M -hyponormal if there exists a positive real number M such that T ? (M 2 (T ??)? (T ??))T ? T ? (T ??)(T ??)? T for all ? ? C, which is a generalization of M -hyponormality. In this paper, we consider the local spectral properties for quasi-M -hyponormal operators and Weyl type theorems for algebraically quasi-M-hyponormal operators, respectively. It is also proved that if T is an algebraically quasi-M -hyponormal operator, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.