Putnam's inequality for log-hyponormal operators
Let \(H\) be a complex Hilbert space and \(B(H)\) the algebra of all bounded linear operators on \(H\). An operator \(T\in B(H)\) is \(p\)-hyponormal if \((T^*T)^p\geq (TT^*)^p\). An operator \(T\in B(H)\) is log-hyponormal if \(T\) is invertible and \(\log(T^*T)\geq\log(TT^*)\) [see \textit{K. Tanahashi}, Integral Equations Oper. Theory 34, No. 3, 364--372 (1999; Zbl 0935.47015)]. In the present paper, the author proves Putnam's inequality for log-hyponormal operators, i.e., if \(T\) is log-hyponormal, then \[ \|\log(T^*T)- \log(TT^*)\|\leq{1\over \pi} \iint_{\sigma(T)} r^{-1}dr\,d\theta. \]
scientific article; zbMATH DE number 2051561