On simpliciality of function spaces not containing constants
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915097822101504 |
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| author | Kalenda, Ondřej F. K. Spurný, Jiří |
| author_facet | Kalenda, Ondřej F. K. Spurný, Jiří |
| contents | We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given point is not represented by any measure pseudosupported by the Choquet boundary, illustrating so limits of possible generalizations of the representation theorem. Moreover, we address the abstract Dirichlet problem in the new setting and establish some common points and nontrivial differences with the classical case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16100 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On simpliciality of function spaces not containing constants Kalenda, Ondřej F. K. Spurný, Jiří Functional Analysis 46A55, 46B04, 28C05 We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given point is not represented by any measure pseudosupported by the Choquet boundary, illustrating so limits of possible generalizations of the representation theorem. Moreover, we address the abstract Dirichlet problem in the new setting and establish some common points and nontrivial differences with the classical case. |
| title | On simpliciality of function spaces not containing constants |
| topic | Functional Analysis 46A55, 46B04, 28C05 |
| url | https://arxiv.org/abs/2401.16100 |