Topology of Gleason Parts in maximal ideal spaces with no analytic discs
| Autor: | Dimitris Papathanasiou, Alexander J. Izzo |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Mathematics - Complex Variables Mathematics::Complex Variables General Mathematics 010102 general mathematics 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis FOS: Mathematics Maximal ideal 0101 mathematics Complex Variables (math.CV) Topology (chemistry) Mathematics |
| DOI: | 10.48550/arxiv.1902.05505 |
| Popis: | We strengthen, in various directions, the theorem of Garnett that every $\sigma$-compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen so that its maximal ideal space contains no analytic discs. We show that when the space $X$ is metrizable, the uniform algebra can be chosen so that its maximal ideal space is metrizable as well. We also show that for every locally compact subspace $X$ of a Euclidean space, there is a compact set $K$ in some ${\mathbb C}^N$ so that $\hat K \setminus K$ contains a Gleason part homeomorphic to $X$ and $\hat K$ contains no analytic discs. Comment: Inaccuracies in the previous version have been corrected |
| Databáze: | OpenAIRE |
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