A nontrivial uniform algebra regular on the Cantor set
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909933113442304 |
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| author | Feinstein, J. F. Izzo, Alexander J. |
| author_facet | Feinstein, J. F. Izzo, Alexander J. |
| contents | We prove the existence of a nontrivial uniform algebra that is logmodular and regular on the Cantor set. As a consequence, we obtain that for every compact metrizable space X without isolated points there exists a nontrivial essential uniform algebra that is logmodular and regular on X. In particular, there exists a nontrivial essential uniform algebra that is logmodular and regular on the closed unit interval. Our algebras seem to be the first known uniform algebras that are regular on a metrizable space but are not normal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nontrivial uniform algebra regular on the Cantor set Feinstein, J. F. Izzo, Alexander J. Complex Variables Functional Analysis Primary 30H50, 46J10, 46J15, Secondary 30H05, 30H10 We prove the existence of a nontrivial uniform algebra that is logmodular and regular on the Cantor set. As a consequence, we obtain that for every compact metrizable space X without isolated points there exists a nontrivial essential uniform algebra that is logmodular and regular on X. In particular, there exists a nontrivial essential uniform algebra that is logmodular and regular on the closed unit interval. Our algebras seem to be the first known uniform algebras that are regular on a metrizable space but are not normal. |
| title | A nontrivial uniform algebra regular on the Cantor set |
| topic | Complex Variables Functional Analysis Primary 30H50, 46J10, 46J15, Secondary 30H05, 30H10 |
| url | https://arxiv.org/abs/2511.14020 |