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 |
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