Powers of operators from any class, including the normal operators, are not in general members of the same class. For instance, if T is a class operator, then is not necessarily a class operator, but if T is an invertible class  operator, all of its powers happen to be class operators. Unlike in class  operators, every power of a w-hyponormal operator is a w-hyponormal operator. In this paper, we investigate the normality of the powers of generalized Aluthge transforms of w-hyponormal operators and that of the generalized Aluthge transforms of the powers of w-hyponormal operators.

normal operators, w-hyponormal, Aluthge transforms, powers.