Stability of [formula omitted]-property for the induced Aluthge transformations

Abstract

We shall show that if a bounded linear operator T on a complex Hilbert space H satisfies AN-property, then the induced Aluthge transformations with respect to some means of T satisfy AN-property, too. Moreover, we shall discuss a limit point of mean transformation. Chabbabi, Curto and Mbekhta pointed out that a sequence of iterated mean transform of an operator with a special condition converges to a normal operator in the strong operator topology without proof. We shall give a proof of iterated mean transformation of a semi-hyponormal operator converges. Moreover, we shall show that the limit point satisfies AN-property if T does so.