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# Composition Operators on Analytic Lipschitz Spaces

Kevin M. Madigan
Proceedings of the American Mathematical Society
Vol. 119, No. 2 (Oct., 1993), pp. 465-473
DOI: 10.2307/2159930
Stable URL: http://www.jstor.org/stable/2159930
Page Count: 9
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## Abstract

If X is a Banach space of functions analytic on the disk and φ: D → D is analytic, one can define the composition operator Cφ 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 $\mathscr{A}_\alpha, 0 < \alpha < 1$.

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