On powers of \(p\)-hyponormal and log-hyponormal operators (Q1585225)

A bounded linear operator \(T\) on a Hilbert space \({\mathcal H}\) is said to be \(p\)-hyponormal for \(p>0\) if \((T^* T)^p\geq (TT^*)^p\) and \(T\) is said to be log-hyponormal if \(T\) is invertible and \(\log T^*T\geq \log TT^*\). In this paper, the authors give some inequalities between the powers of \(p\)-hyponormal operators and also log-hyponormal operators.