Some spectral properties of quasi-dominant operators

In this paper, we introduce a new class of operators called the class of quasi-dominant operators. This class includes hyponormal, [Formula: see text]-hyponormal and dominant operators. Our results are motivated by several known properties of [Formula: see text]-quasi-[Formula: see text]-hyponormal operators [F. Zuo and S. Mecheri, Spectral properties of [Formula: see text]-quasi-[Formula: see text]-hyponormal operators, Complex Anal. Oper. Theory 12 (2018) 1877–1887], then by those of normal operators. Besides we study the local spectral properties for this class of operators.