Norms and spectral radii of composition operators acting on the Dirichlet space |
| |
| Authors: | Marí a J. Martí n |
| |
| Affiliation: | a Departamento de Economía, Universidad Carlos III, C/ Madrid 126, 28903 Getafe (Madrid), Spain
b Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain |
| |
| Abstract: | We obtain new upper bounds on the norms of univalently induced composition operators acting on the Dirichlet space and compute explicitly the norms for univalent symbols whose range is the disk minus a set of measure zero. As an application, we show that the spectral radius of every univalently induced composition operator on the Dirichlet space is equal to one. |
| |
| Keywords: | Dirichlet space Composition operator Operator norm Spectral radius Hyperbolic metric |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
