Composition and Volterra-type inner derivations on the generalized Fock spaces

Abstract

A classical result of Calkin \cite{Cjw} says that the inner derivation maps the algebra of bounded operators on a Hilbert space into the ideal of compact operators if and only if the induced operator is a compact perturbation of the scalar operator. On the generalized Fock spaces, we use the compact intertwing relations to study the range of the inner derivations induced by the composition operators $C_{\varphi}$ and the Volterra type operators $J_g$ and $I_g$.