  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 conclude that, invertible weighted conditional
type operators are normal. In the end we give some appli- cations of
p-hyponormal weighted conditional type operators. In the end, some examples are
provided to illustrate concrete application of the main results of the paper.
