Integral Equations and Operator Theory

, Volume 45, Issue 1, pp 1–14

Connected components in the space of composition operators onH∞ functions of many variables

  • Richard Aron
  • Pablo Galindo
  • Mikael Lindström
Integral Equations and Operator Theory

DOI: 10.1007/BF02789591

Cite this article as:
Aron, R., Galindo, P. & Lindström, M. Integr equ oper theory (2003) 45: 1. doi:10.1007/BF02789591

Abstract

LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.

2000 AMS Classification Numbers

Primary 46J15 Secondary 46E15, 46G20 

Copyright information

© BirkhÄuser Verlag 2003

Authors and Affiliations

  • Richard Aron
    • 1
  • Pablo Galindo
    • 2
  • Mikael Lindström
    • 3
  1. 1.Department of MathematicsKent State UniversityKentUSA
  2. 2.Departamento de Análisis MatemáticoUniversidad de ValenciaValenciaSpain
  3. 3.Department of MathematicsAbo Akademi UniversityAboFinland

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