A characterization of composition operators on algebras of analytic functions

DANIEL CARANDO

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

CAMBRIDGE UNIV PRESS

Año: 2008

0013-0915

We give a characterization of composition operators between algebrasof analytic functions on a Banach space. We show (under fairlygeneral conditions) that they are precisely the multiplicativeoperators that are transposes of operators of between the predualsof the algebras. The special cases of $H^infty(U)$ and $H_b(U)$ areconsidered. In this cases, composition operators are those which arepointwise to pointwise continuous and (or) $ au_0$ to $ au_0$continuous (where $ au_0$ is the compact-open topology). We obtainBanach-Stone type theorems for these algebras.