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Isometric composition operators on the weighted Hardy spaces

✍ Scribed by Nizar Jaoua

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
96 KB
Volume
283
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We investigate the composition operators on the weighted Hardy spaces H^2^(β). For any bounded weight sequence β, we give necessary conditions for those operators to be isometric. The sufficiency of those conditions is well‐known for the classical space H^2^. In the case where β is non‐decreasing or non‐increasing, their sufficiency holds only for very few weighted spaces. We find out such spaces by characterizing the isometric monomial composition operators, first for a general β, then for any β as before. With no restriction on β, we provide a complete description of all isometric composition operators. We also prove that the unitary monomial ones are the same as those acting on H^2^. Such a fact extends to general symbols in the case where β is bounded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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