Extensions of the results on ρ-hyponormal and log-hyponormal operators by Aluthge and Wang

Abstract

Aluthge and Wang [4] showed that “if $T$ is $p$-hyponormal then $T^n$ is $\left(\frac{p}{n}\right)$-hyponormal for $p\in (0,1]$”. Firstly we obtain precise estimation of this result. Secondly we show that “if $T$ is log-hyponormal then $T^n$ is log-hyponormal” and this result is an extension of Theorem B by Aluthge and Wang [3].