On the class of k-quasi-(n, m)-power normal operators

We introduce a new class of operators which we will be called the class of k-quasi-(n;m)-power normal operators that includes normal, n-normal and (n;m)- power normal operators. In this paper, firstly some basic structural properties of this class of operators are established with the help of special kind of operator matrix representation associated with such operators. Secondly, some properties of algebraically k-quasi-(n;m)-power normal operators are discussed. Thirdly, we consider the tensor products for k-quasi-(n;m)-power normal operators, giving a necessary and sufficient condition for T S to be a k-quasi-(n;m)-power normal operator when T and S are both nonzero operators.