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
operator $M_wEM_u$ is $p$-hyponormal if and only if it is normal,
and under a weak condition, if $M_wEM_u$ 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.