Connected components in the space of composition operators onH∞ functions of many variables
- Cite this article as:
- Aron, R., Galindo, P. & Lindström, M. Integr equ oper theory (2003) 45: 1. doi:10.1007/BF02789591
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.