Isolated points and essential components of composition operators on 𝐻^{∞}

Hosokawa, Takuya; Izuchi, Keiji; Zheng, Dechao

doi:10.1090/S0002-9939-01-06233-5

Isolated points and essential components of composition operators on $H^\infty$
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by Takuya Hosokawa, Keiji Izuchi and Dechao Zheng

Proc. Amer. Math. Soc. 130 (2002), 1765-1773

DOI: https://doi.org/10.1090/S0002-9939-01-06233-5

Published electronically: October 24, 2001

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Abstract:

We consider the topological space of all composition operators on the Banach algebra of bounded analytic functions on the unit disk. We obtain a function theoretic characterization of isolated points and show that each isolated composition operator is essentially isolated.

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