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 |
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Keywords
- Dirichlet algebras
- Fibers
- Gleason parts
- Maximal ideal spaces
- Minimal flows
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Flows in fibers. / Tanaka, Junichi.
In: Transactions of the American Mathematical Society, Vol. 343, No. 2, 1994, p. 779-804.Research output: Contribution to journal › Article
}
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 -