SOME PROPERTIES OF (n, m)-POWER-HYPONORMAL IN SEMI HILBERTIAN SPACE

Abstract

In [1] (Kikete Wabuya, Luketero Wanyonyi, and Justus Mile) show that if an operator (n,m) hyponormal is isometrically equivalent to an operator S, then S is also (n ,m) hyponormal operator. In this paper, we prove results in the same spirit but in a semi Hilbertian space, i.e., spaces generated by positive semi-definite sesquilinear forms. This kind of spaces appears in many problems concerning linear and bounded operators on Hilbert spaces and is intensively studied in the present; some of the basic properties of this class are studied. Moreover, the product, tensor product and the sum of finite numbers of this type are discussed.