A nontrivial uniform algebra regular on the Cantor set
Complex Variables
2025-12-02 v2 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2511.14020,
title = {A nontrivial uniform algebra regular on the Cantor set},
author = {J. F. Feinstein and Alexander J. Izzo},
journal= {arXiv preprint arXiv:2511.14020},
year = {2025}
}
Comments
Many details of the exposition have been polished since the original submission