Properties of quasi-invariant measures on topological groups and associated algebras
type: Item
instance of: scholarly article
title: Properties of quasi-invariant measures on topological groups and associated algebras
zbMATH Open document ID: 0936.22004
published in: Annales Mathématiques Blaise Pascal
publication date: 2000-05-02T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79206
review text: Let \(G\) be a topological group, \(H\) its invariant subgroup and \(\mu \) a measure defined on the completion \(Af( G,\mu) \) of the Borel \(\sigma \)-field of \(G\). Then \(\mu \) is called left-quasi-invariant provided \(\mu _{h}\) is equivalent to \(\mu \) for each \( h\in H\), where \(\mu _{h}( A) :=\mu ( h^{-1}A) \) for each \(A\in Af( G,\mu) \). The author studies: a) weakly continuous (weakly measurable) representations of a topological group \(G\) with a left-quasi-invariant measure; b) maximal ideals of a non-associative Banach algebra associated to a topological group which possesses a decreasing sequence of subgroups with left-quasi-invariant measures.
Mathematics Subject Classification ID: 22A10
Mathematics Subject Classification ID: 43A05
zbMATH DE Number: 1331689
zbMATH Keywords: left-quasi-invariant measure
zbMATH Keywords: weakly continuous representation
author: Sergey V. Ludkovsky
reviewed by: Mihail I. Ursul
MaRDI profile type: Publication
OpenAlex ID: W2038992745
cites work: Q4115334
cites work: Q4002453
cites work: Q3994935
cites work: Q5565773
cites work: Q4039914
cites work: Irreducible regular Gaussian representations of the groups of the interval and circle diffeomorphisms
cites work: Gaussian measures in Banach spaces
cites work: Measures on groups of diffeomorphisms of non-Archimedean Banach manifolds
cites work: Measurability of representations of locally compact groups
cites work: Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications
cites work: Quasi-invariant measures on non-Archimedean semigroups of loops
cites work: Q4519769
cites work: Generalized geometric loop groups of complex manifolds, Gaussian quasi-invariant measures on them and their representations
cites work: Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations. I
cites work: Q3262469
cites work: Q3803294
cites work: Q3484051
DOI: 10.5802/AMBP.113
description: scientific article; zbMATH DE number 1331689