Powers of an Invertible (s, p)—w—Hyponormal Operator

It is known that the square of a w–hyponormal operator is also w–hyponormal. For any 0 < p < 1, there exists a special invertible operator such that all of its integer powers are all p – w–hyponormal. In this article, the author introduces the class of (s, p) – w–hyponormal operators on the basis of the class of p – w–hyponormal operators. For s>0, 0 < p < 1, the author gives a characterization of (s, p) – w–hyponormal operators; the author shows that all integer powers of special (s, p) – w–hyponormal operators are (s, p) – w–hyponormal.