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.
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Karanu et al. (2024) studied this question.
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