### 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 language | English |
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Pages (from-to) | 779-804 |

Number of pages | 26 |

Journal | Transactions of the American Mathematical Society |

Volume | 343 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1994 |

Externally published | Yes |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Tanaka, J. (1994). Flows in fibers.

*Transactions of the American Mathematical Society*,*343*(2), 779-804. https://doi.org/10.1090/S0002-9947-1994-1202421-8