On m-quasi class A(k∗) and absolute-(k∗,m)-paranormal operators

Abstract

In this paper, we introduce a new class of operators, called m-quasi class A(k∗) operators, which is a superclass of hyponormal operators and a subclass of absolute-(k∗,m)-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that if T is m-quasi class A(k∗), then σnp(T) {0} = σp(T) {0}, σna(T) {0} = σa(T) {0} and T − µ has nite ascent for all µ ∈C. Also, we consider the tensor product of m-quasi class A(k∗) operators.