Inversion quasi-invariant Gaussian measures on the group of upper-triangular matrices of infinite order
type: Item
instance of: scholarly article
title: Inversion quasi-invariant Gaussian measures on the group of upper-triangular matrices of infinite order
zbMATH Open document ID: 0961.43001
DOI: 10.1007/BF02467071
publication date: 2001-05-06T00:00:00Z
review text: In [Measures on infinite-dimensional groups, quasi-invariant with respect to inverse mapping and the commutant theorem (Singapore 1998; Zbl 0935.43001)], the author presented a scheme for generalising, to non-locally compact groups, the commutation theorem for locally compact groups with (left) Haar measure, viz. that the right regular representation is generated by the operators of the left regular representation. He showed that, for \({\tilde{G}}\) the group of upper triangular infinite matrices, which he provides with a Gaussian measure with variance determined by a double sequence \(b = (b_{k,n})_{k<n}\) of positive numbers, if \(E(b)\), as defined there, is finite then the measure is quasi-invariant with respect to the inverse mapping and an analogue of the commutation theorem holds. The article under review provides a slightly modified version of the proof.
reviewed by: Aubrey Wulfsohn
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 1497245
zbMATH Keywords: left and right regular representations of a group
zbMATH Keywords: quasi-invariant Gaussian measure
zbMATH Keywords: upper triangular infinite matrices
zbMATH Keywords: locally compact groups
zbMATH Keywords: commutation theorem
author: A. V. Kosyak
MaRDI profile type: Publication
cites work: Rigid isotopy classification of real plane curves of degree 5
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: Irreducible regular Gaussian representations of the groups of the interval and circle diffeomorphisms
cites work: Conditions necessary for optimality in the convex Bolza problem with phase constraints of a general form
cites work: Gaussian measures in Banach spaces
cites work: Q4064239
full work available at URL: https://doi.org/10.1007/bf02467071
OpenAlex ID: W2082163280
Recommended article: Invertion of infinite Gaussian matrices
Recommended article: Q4258052
Recommended article: Q3472906
Recommended article: Quasi-invariant measures on the orthogonal group over the Hilbert space
Recommended article: Invariant or quasi-invariant probability measures for infinite dimensional groups. II: Unitarizing measures or Berezinian measures
Recommended article: On the inversion of infinite moment matrices
Recommended article: Invariant and quasi-invariant measures on infinite-dimensional spaces
Recommended article: Q4366845
Recommended article: Quasi-invariant measures on commutative Lie groups of infinite product type
Recommended article: Q3686951
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1497245