A unitarization process for some non-locally compact topological groups
type: Item
instance of: scholarly article
title: A unitarization process for some non-locally compact topological groups
zbMATH Open document ID: 0790.22011
DOI: 10.1007/BF02572400
author: V. Pereyra
published in: Mathematische Zeitschrift
publication date: 1994-06-22T00:00:00Z
full work available at URL: https://eudml.org/doc/174564
review text: The notion of Polish environment of quasi invariance (for short: a PEQI) for a non-locally compact topological group is introduced, which generalizes in some sense the notion of Wiener-Lie group as it is shown by giving some examples among current groups. A non-locally compact topological group \(G\) equipped with a PEQI has a left regular unitary representation; it is proved that there exists a unitarization process which associates a cyclic continuous unitary representation of \(G\) with each locally bounded representation of the PEQI.
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 58D20
zbMATH DE Number: 567437
zbMATH Keywords: Borel measure
zbMATH Keywords: Polish group
zbMATH Keywords: Polish environment of quasi invariance
zbMATH Keywords: non- locally compact topological group
zbMATH Keywords: Wiener-Lie group
zbMATH Keywords: current groups
zbMATH Keywords: unitary representation
zbMATH Keywords: locally bounded representation
MaRDI profile type: Publication
cites work: Irreducibility and reducibility for the energy representation of the group of mappings of a Riemannian manifold into a compact semisimple Lie group
cites work: Factorial representations of path groups
cites work: Q3256687
cites work: Stochastic differential geometry
cites work: Q3897751
cites work: Gaussian measures in Banach spaces
cites work: Group representations. A survey of some current topics
cites work: Integration on loop groups. I: Quasi invariant measures
cites work: Q4840473
cites work: Infinite dimensional Lie transformation groups
cites work: Q5533878
description: scientific article; zbMATH DE number 567437