k - Quasi - Normal Operators

In this paper, a new class of operator, k Quasi normal is defined as T (T ∗T )k = (T ∗T )kT and some properties on it are discussed. This k Quasi normal operator is introduced as a generalization of concept of Quasi normal. The k Quasi normal operators are also characterized in terms of commutativity with the multiplication operator induced by the Radon Nikodym derivative of the measure λ(T k)−1 with respect to λ.