Properties of log-hyponormal operators (Q1401615)

For a complex Hilbert space \(H\), the algebra of all bounded linear operators on \(H\) is denoted by \({\mathcal L}(H)\), and \(T\in{\mathcal L}(H)\) is called log-hyponormal if it is invertible and \(\log(TT^*)\leq\log(T^*T)\). Among other properties, it is shown that each log-hyponormal operator is subscalar of order 2, i.e., it is similar to the restriction of an operator \(S\) on \(H\) for which there exists a continuous unital morphism of topological algebras \(\phi: C^2_0(\mathbb{C})\to{\mathcal L}(H)\) such that \(\phi(\text{id})= S\).