2012/11/18 by Paul Bourdon, Paul S. Bourdon, Bourdon, Paul S.
Mathematics · #47B33 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.FA #msc:47B33
paper · pdf · doi:10.48550/arxiv.1211.4190
11 pages, to be published in the Proceedings of the American Mathematical Society
arxiv created 2012/11/18 · openalex publication_date 2012/11/18 · arxiv updated 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is invertible on X, then phi is an automorphism of D, and we derive a similar result for mappings of the form f |-> psi.(f o phi), where psi is some analytic function on D. We obtain as corollaries of this purely function-theoretic work, new results concerning invertibility of composition operators and weighted composition operators on Banach spaces of analytic functions such as Sp and the weighted Hardy spaces H2(beta).