Connected components in the space of composition operators on H functions of many variables

Richard Aron*, Pablo Galindo, Mikael Lindström

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

17 Citations (Scopus)

Abstract

Let E be a complex Banach space with open unit ball BE. The structure of the space of composition operators on the Banach algebra H(BE), of bounded analytic functions on BE with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly inside BE form a path connected component. When E is a Hilbert space or a C0(X)-space, the path connected components are shown to be the open balls of radius 2.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalIntegral Equations and Operator Theory
Volume45
Issue number1
DOIs
Publication statusPublished - 2003
MoE publication typeA1 Journal article-refereed

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