Probability measures on [SIN] groups and some related ideals in group algebras

• Published in: Monatshefte für Mathematik Vol. 155; no. 2; pp. 135 - 144
• Main Author: Jaworski, Wojciech
• Format: Journal Article
• Language: English
• Published: Vienna Springer-Verlag 01.10.2008; Springer Nature B.V
• Subjects: Mathematics; Mathematics and Statistics; Key words: Probability measures, random walks, locally compact groups, SIN groups, group algebras, ideals, amenability; 2000 Mathematics Subject Classification: 60B15, 22D15, 43A05, 43A07
• ISSN: 0026-9255; 1436-5081
• DOI: 10.1007/s00605-008-0544-2

. Given a locally compact group G , let denote the set of closed left ideals in L 1 ( G ), of the form J μ = [L 1 ( G ) * (δ e − μ)] − , where μ is a probability measure on G . Let , . When G is a second countable [SIN] group, we prove that and that , being a proper subset of when G is nondiscrete, contains every maximal element of . Some results concerning the ideals J μ in general locally compact second countable groups are also obtained.