Separating classes of composition operators via subnormal condition

Abstract

Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is n-hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider E(n)-hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize E(n)-hyponormality of composition operators via k-th Radon-Nikodym derivatives and present some examples to distinguish the classes. © 2007 American Mathematical Society.