On quasi-\(A(n,k)\) class operators (Q2868487)

In this paper, the so-called quasi-\(A(n,k)\) class operator (defined by \(T^{\ast k}|T^{n}|T^{k}\geq T^{\ast k}|T|^{n}T^{k}\)) for \(n\geq2\) and \(k\geq 0\) is introduced as a new notion, which generalizes the notion of quasi-class \(A\) operator. Some structural properties of these operators are considered. A model to distinguish quasi-\(A(n, k)\) operators is given via weighted shift operators, and a simple example of quasi-\(A(n,k)\) operators with two variables is presented.