Abstract. In this paper, we shall define $*$-Aluthge transformation (i.e., $\widetilde{T}^{(*)}=|T^*|^{1/2}U|T^*|^{1/2}$), and show some properties of it. Next, we shall show parallelisms between Aluthge transformation and powers of $p$-hyponormal operators, $\log $-hyponormal operators and $w$-hyponormal operators by using $*$-Aluthge transformation.

AMS Subject Classification (1991): 47B20, 47A63

Received September 12, 2000. (Registered under 2819/2009.)