On Unitary Quasi-Equivalence and w-Hyponormal Operators In Hilbert Spaces

In this paper, the properties of unitary quasi-equivalence on the class of w-hyponormal operators are presented using the Aluthge transform and polar decomposition property. We show that for any two unitary quasi-equivalent operators, F and G, if one is w-hyponormal, then the other operator is also w-hyponormal. This result also holds for p-hyponormal and log-hyponormal operators.