Connected components in the space of composition operators onH∞ functions of many variables |
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Authors: | Richard Aron Pablo Galindo Mikael Lindström |
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Affiliation: | (1) Department of Mathematics, Kent State University, 44242 Kent, Ohio, USA;(2) Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjasot, Valencia, Spain;(3) Department of Mathematics, Abo Akademi University, FIN-20500 Abo, Finland |
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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. 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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Keywords: | Primary 46J15 Secondary 46E15, 46G20 |
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