Compact Differences of Composition Operators on Bloch and Lipschitz Spaces | Zendy

Pekka Nieminen | Zendy

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Compact Differences of Composition Operators on Bloch and Lipschitz Spaces

Author(s) -

Pekka Nieminen

Publication year - 2007

Publication title -

computational methods and function theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.627

H-Index - 16

eISSN - 2195-3724

pISSN - 1617-9447

DOI - 10.1007/bf03321648

Subject(s) - compact space , mathematics , bloch space , lipschitz continuity , composition (language) , composition operator , banach space , pure mathematics , operator (biology) , compact operator , mathematical analysis , discrete mathematics , finite rank operator , biochemistry , gene , philosophy , linguistics , chemistry , repressor , transcription factor , computer science , extension (predicate logic) , programming language

We consider the dierence T = C C of two analytic composition operators in the unit disc. We characterize the compactness and weak compact- ness of T on the standard Bloch space, improving an earlier result by Hosokawa and Ohno. We also characterize the compactness and weak compactness of T on analytic Lipschitz spaces. These characterizations are derived from a general result dealing with dierences of weighted composition operators on weighted Ba- nach spaces of analytic functions. We also make complementary remarks on the compactness properties of a single composition operator on the Lipschitz spaces.

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