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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Composition operators on analytic Lipschitz spaces


Author: Kevin M. Madigan
Journal: Proc. Amer. Math. Soc. 119 (1993), 465-473
MSC: Primary 47B38; Secondary 30H05, 46E15, 47B07
MathSciNet review: 1152987
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Abstract: If $ X$ is a Banach space of functions analytic on the disk and $ \varphi :{\mathbf{D}} \to {\mathbf{D}}$ is analytic, one can define the composition operator $ {C_\varphi }$ on $ X$ by $ {C_\varphi }f: = f \circ \varphi $. This paper discusses the boundedness and $ w$-compactness of composition operators on the analytic Lipschitz spaces $ {\mathcal{A}_\alpha },\;0 < \alpha < 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152987-6
PII: S 0002-9939(1993)1152987-6
Article copyright: © Copyright 1993 American Mathematical Society