Abstract
LetE be a complex Banach space with open unit ballB e. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onB e with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideB e form a path connected component. WhenE is a Hilbert space or aC o(X)- space, the path connected components are shown to be the open balls of radius 2.
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The research of this author was supported by grant number SAB1999-0214 from the Ministerio de Educación, Cultura y Deporte during his stay at the Universidad de Valencia.
The research of this author was partially supported DGES(Spain) pr. 96-0758.
The research of this author was partially supported by Magnus Ehrnrooths stiftelse.
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Aron, R., Galindo, P. & Lindström, M. Connected components in the space of composition operators onH∞ functions of many variables. Integr equ oper theory 45, 1–14 (2003). https://doi.org/10.1007/BF02789591
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DOI: https://doi.org/10.1007/BF02789591