### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*343*(2), 779-804. https://doi.org/10.1090/S0002-9947-1994-1202421-8

**Flows in fibers.** / Tanaka, Junichi.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 343, no. 2, pp. 779-804. https://doi.org/10.1090/S0002-9947-1994-1202421-8

}

TY - JOUR

T1 - Flows in fibers

AU - Tanaka, Junichi

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - Dirichlet algebras

KW - Fibers

KW - Gleason parts

KW - Maximal ideal spaces

KW - Minimal flows

UR - http://www.scopus.com/inward/record.url?scp=84966203801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966203801&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1994-1202421-8

DO - 10.1090/S0002-9947-1994-1202421-8

M3 - Article

AN - SCOPUS:84966203801

VL - 343

SP - 779

EP - 804

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -