On a class of operators with normal Aluthge transformations

Abstract

In this paper, we show that the generalized Aluthge transformations of a large class of operators (weighted conditional type operators) are normal. As a consequence, the operatorMwEMu 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, for instance, point spectrum and joint point spectrum of p-hyponormal weighted conditional type operators are equal. In the end, some examples are provided to illustrate concrete application of the main results of the paper. <br><br><font color="red"><b> This article has been retracted. Link to the retraction <u><a href="http://dx.doi.org/10.2298/FIL1601253E">10.2298/FIL1601253E</a><u></b></font>