Characterization, structure and analysis on Abelian \({\mathcal L}_{\infty}\) groups
type: Item
instance of: scholarly article
title: Characterization, structure and analysis on Abelian \({\mathcal L}_{\infty}\) groups
zbMATH Open document ID: 0563.43005
DOI: 10.1007/BF01383716
author: Rangachari Venkataraman
published in: Monatshefte für Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178237
review text: An abelian topological group is an \({\mathcal L}_{\infty}\) group if and only if it is a locally \(\sigma\)-compact k-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian \({\mathcal L}_{\infty}\) group G is topologically isomorphic to \({\mathbb{R}}^{\alpha}\oplus G_ 0\) where \(\alpha \leq \aleph_ 0\) and \(G_ 0\) is an abelian \({\mathcal L}_{\infty}\) group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra, \(L_ 1\)-algebra, Fourier transforms of abelian \({\mathcal L}_{\infty}\) groups are given and their properties are studied.
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 3897561
zbMATH Keywords: \({\mathcal L}_{\infty }\) group
zbMATH Keywords: convolution
zbMATH Keywords: \(L_ 1\)-algebra
zbMATH Keywords: Fourier transforms
MaRDI profile type: Publication
cites work: Q5522002
cites work: Countable products and sums of lines and circles: their closed subgroups, quotients and duality properties
cites work: Q5183974
cites work: A remark on characters of locally compact Abelian groups
cites work: Q5723435
cites work: Extensions of the Pontrjagin duality. I: Infinite products
cites work: Extensions of the Pontrjagin duality. II: Direct and inverse sequences
cites work: On Countable Inductive Limits of Locally Compact Abelian Groups
cites work: Q5545817
cites work: Coproduct in the category of groups satisfying Pontryagin duality
description: scientific article; zbMATH DE number 3897561