On Aluthge Transforms of p-hyponormal Operators

Abstract.

In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform $\widetilde T$ is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence $\{ \widetilde T^{{(n)}} \} ^{\infty }_{{n = 1}}$ of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6].