On the relation between the scalar moment problem and the matrix moment problem on *-semigroups
type: Item
instance of: scholarly article
title: On the relation between the scalar moment problem and the matrix moment problem on *-semigroups
zbMATH Open document ID: 1045.43009
author: Torben Maack Bisgaard
published in: Semigroup Forum
publication date: 2004-07-01T00:00:00Z
review text: The author presents an example of a commutative \(*\)-semigroup with identity which is semiperfect of order~\(1\) but not of order~\(2\). Here, a commutative \(*\)-semigroup \(S\) is called semiperfect of order \(d\) (where \(d\) is a positive integer) if every matrix-valued function \(f: S\to M_d({\mathbb C})\) of positive type is of the form \(f(s)=\int_{S^*}\sigma(s)\, d\mu(\sigma)\) for some \(M_d({\mathbb C})_+\)-valued measure~\(\mu\) on the space \(S^*\) of characters of~\(S\) (i.e., non-zero, hermitian, multiplicative functions on~\(S\)).
Mathematics Subject Classification ID: 43A35
zbMATH DE Number: 2077983
zbMATH Keywords: scalar moment problem
zbMATH Keywords: matrix moment problem
zbMATH Keywords: functions of positive type
zbMATH Keywords: positive definite functions
zbMATH Keywords: representing measures
zbMATH Keywords: semiperfect semigroups
MaRDI profile type: Publication
full work available at URL: s00233-002-0003-7
OpenAlex ID: W2096549693
DOI: 10.1007/S00233-002-0003-7
description: scientific article; zbMATH DE number 2077983