Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Acuaviva, Antonio
Institution: Lancaster University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214383422