Flows in fibers

Junichi Tanaka

doi:10.1090/S0002-9947-1994-1202421-8

Flows in fibers

Junichi Tanaka

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	779-804
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	343
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1994-1202421-8
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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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.

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KW - Gleason parts

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KW - Minimal flows

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Flows in fibers

Abstract

Keywords

ASJC Scopus subject areas

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