On a Generalization of Quasiposinormal Operators

Paper describes some properties for the operators $A$ on a Hilbert space $\mathcal{H}$ satisfying $(A^*A)^k \le c^2A^{*k}A^k$ for some $c > 0, k \ge 2$ and also presents some characterizations for the composition operators and the weighted composition operators on the Hilbert space $L^2$ to be of this type.