Substitution of open subhypergroups
type: Item
instance of: scholarly article
title: Substitution of open subhypergroups
zbMATH Open document ID: 0821.43004
author: Michael Voit
published in: Hokkaido Mathematical Journal
publication date: 1995-09-19T00:00:00Z
review text: Hypergroups generalize locally compact groups. If the Banach space of all bounded Radon measures on a locally compact space \(X\) carries a convolution structure satisfying some properties the space \(X\) is called hypergroup. Details and many examples are contained in the recent monograph of Bloom and Heyer. In the present paper the author generalizes the construction of so-called joins. The join \(L \vee K\) of a compact hypergroup \(L\) and a discrete hypergroup \(K\) is formed by replacing the unit element of \(K\) by the hypergroup \(L\). This method is extended as follows: If \(H\) is an open subhypergroup of a hypergroup \(K\), and \(\pi\) is an open and proper hypergroup homomorphism from a further hypergroup \(L\) onto \(H\), then on the disjoint union of \(K - H\) and \(L\) is defined a natural hypergroup structure. The author calls this procedure substitution of \(H\) by \(L\) in \(K\). After the construction of hypergroups formed by substitution positive definite functions and irreducible representations are studied. Further the dual space is investigated in the commutative case. Finally the author describes some classes of hypergroups via substitution.
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 43A40
Mathematics Subject Classification ID: 43A35
zbMATH DE Number: 569385
zbMATH Keywords: locally compact groups
zbMATH Keywords: bounded Radon measures
zbMATH Keywords: disjoint union
zbMATH Keywords: substitution
zbMATH Keywords: positive definite functions
zbMATH Keywords: irreducible representations
zbMATH Keywords: dual spaces
reviewed by: Rupert Lasser
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381412491
OpenAlex ID: W1969314498
DOI: 10.14492/HOKMJ/1381412491
description: scientific article; zbMATH DE number 569385