PreprintCC BY-NC-ND 4.0arXiv
A solution to Michael's problem for Fréchet algebras
Abstract
We prove that every character on a commutative complex complete Hausdorff locally multiplicatively convex algebra, not necessarily unital, is bounded on bounded sets. Consequently, every character on a commutative complex Fréchet--Arens--Michael algebra is continuous, giving an affirmative answer to Michael's problem. In the Fréchet case, each character is bounded by one seminorm from any increasing defining sequence of submultiplicative seminorms.
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BibTeX
@misc{acuaviva2026solution,
title = {{A solution to Michael's problem for Fréchet algebras}},
author = {Antonio Acuaviva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28584},
eprint = {2609.28584},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28584},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A solution to Michael's problem for Fréchet algebras
AU - Antonio Acuaviva
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28584
UR - https://arxiv.org/abs/2609.28584
AB - We prove that every character on a commutative complex complete Hausdorff locally multiplicatively convex algebra, not necessarily unital, is bounded on bounded sets. Consequently, every character on a commutative complex Fréchet--Arens--Michael algebra is continuous, giving an affirmative answer to Michael's problem. In the Fréchet case, each character is bounded by one seminorm from any increasing defining sequence of submultiplicative seminorms.
ER -