Flows in fibers

Junichi Tanaka

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let be the algebra of all bounded analytic functions on the open unit disc Δ, and let be the maximal ideal space of Using a flow, we represent a reasonable portion of a fiber in This indicates a relation between the corona theorem and the individual ergodic theorem. As an application, we answer a question of Forelli [3] by showing that there exists a minimal flow on which the induced uniform algebra is not a Dirichlet algebra. The proof rests on the fact that the closure of a nonhomeomorphic part in may contain a homeomorphic copy of Taking suitable factors, we may construct a lot of minimal flows which are not strictly ergodic.

Original languageEnglish
Pages (from-to)779-804
Number of pages26
JournalTransactions of the American Mathematical Society
Volume343
Issue number2
DOIs
Publication statusPublished - 1994
Externally publishedYes

Keywords

  • Dirichlet algebras
  • Fibers
  • Gleason parts
  • Maximal ideal spaces
  • Minimal flows

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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