Abelian topological groups without irreducible Banach representations

zbMATH Open0915.22004arXivfunct-an/9708004MaRDI QIDQ4214884

Publication date: 28 June 1999

Abstract: We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach-Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.

Full work available at URL: https://arxiv.org/abs/funct-an/9708004

zbMATH Keywords

topological group character torsion subgroup locally compact group monothetic group minimally almost periodic group Banach-Lie groups Gelfand-Raĭkov's theorem irreducible Banach representation

Mathematics Subject Classification ID

Representations of general topological groups and semigroups (22A25) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65)