A CLASSES OF OPERATORS WITH NORMAL ALUTHGE TRANSFORMATION

Abstract

In this paper, we show that the generalized Aluthge transforma-

tions of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operator MwEMu is p-hyponormal if and only if it is normal, and under a weak condition, if

MwEMu is normal, then the Holder inequality turn into equality for 

w; u. Also, we give some applications of p-hyponormal weighted conditional type operators. In the end, some exam- ples are provided to illustrate concrete application of the main results of the paper.