A Tannaka–Krein extension theorem for topological semigroups
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 243-260
MSC: Primary 22A20; Secondary 43A60, 46L05, 20C15, 43A65.
DOI: 10.4064/cm8968-12-2022
Published online: 18 January 2023
Abstract
We prove a Tannaka–Krein extension theorem for linear mappings taking values in $C^*$-algebras, that are defined on algebras of trigonometric polynomials on topological semigroups. We discuss an application of this result to an approximation problem on the character space of a topological semigroup.
