Cyclical elements of operators which are left-inverses to multiplication by an independent variable

Abstract

We study properties of operators which are left-inverses to the operator of multiplication by an independent variable in the space $\mathcal H (G)$ of functions that are analytic in an arbitrary domain $G$. This space is endowed with topology of compact convergence. A description of cyclic elements for such operators is obtained. The obtained statements generalize known results in this direction.