A characterization of composition operators on algebras of analytic functions - Carando, Daniel Germán (2008)
We give a characterization of composition operators between algebras of analytic functions on a Banach space. We show (under fairly general conditions) that they are precisely the multiplicative operators that are transposes of operators of between the preduals of the algebras. The special cases of $H^∞(U)$ and $H_{b}(U)$ are considered. In these cases, the composition operators are those which are pointwise-to-pointwise continuous and/or $τ_0$-to-$τ_0$ continuous (where $τ_0$ is the compact-open topology). We obtain Banach–Stone-type theorems for these algebras.