Isometric composition operators on the weighted Hardy spaces | Zendy

Jaoua Nizar | Zendy

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Isometric composition operators on the weighted Hardy spaces

Author(s) -

Jaoua Nizar

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200710159

Subject(s) - mathematics , hardy space , composition (language) , bounded function , monomial , isometric exercise , composition operator , unitary state , pure mathematics , space (punctuation) , operator theory , combinatorics , finite rank operator , mathematical analysis , banach space , computer science , medicine , philosophy , linguistics , political science , law , physical therapy , operating system

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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