Composition operators on analytic Lipschitz spaces

Madigan, Kevin M.

doi:10.1090/S0002-9939-1993-1152987-6

Composition operators on analytic Lipschitz spaces
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by Kevin M. Madigan

Proc. Amer. Math. Soc. 119 (1993), 465-473

DOI: https://doi.org/10.1090/S0002-9939-1993-1152987-6

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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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Distances and Banach spaces of holomorphic functions on complex domains