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Isometries of the Dirichlet space among the composition operators |
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| Authors: | Marí a J. Martí n Dragan Vukotic |
| Affiliation: | Departamento de Economía, Universidad Carlos III de Madrid, Calle Madrid 126, 28903 Getafe (Madrid), Spain ; Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain |
| Abstract: | We show that every composition operator which is an isometry of the Dirichlet space is induced by a univalent full map of the disk into itself that fixes the origin. This is an analogue of the Hardy space result for inner functions due to Nordgren. The proof relies on the Stone-Weierstrass theorem and the Riesz representation theorem. |
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