2025/11/18 by Feinstein, J. F., Izzo, Alexander J.
Mathematics · Computer Science · #Advanced Banach Space Theory #Advanced Algebra and Logic #Advanced Operator Algebra Research
paper · doi:10.48550/arxiv.2511.14020
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.