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

Hua He, Xueyan Yang, Zicong Yang

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 $I_g$.


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