Pseudo-characters and almost multiplicative functionals
type: Item
instance of: scholarly article
title: Pseudo-characters and almost multiplicative functionals
zbMATH Open document ID: 0958.43001
author: Félix Cabello Sánchez
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-04-04T00:00:00Z
review text: The main subject studied in the paper under review is the so called stable approximability of the set of characters or continuous characters on a group, i.e. the question whether they can uniformly on \(G\) approximate every almost character. Theorem 1 asserts that on an amenable locally compact group every measurable \(\varepsilon\)-character can uniformly be approximated on \(G\) by continuous characters. The logarithms of multiplicative pseudo-characters can be chosen to be some real additive almost characters (Theorem 2) and in Theorem 3 the author shows that the involutive Banach group algebra \(\ell_1(G)\) is an AMNM (i.e. ``algebra on which almost multiplicative functionals are near to multiplicative functionals'') if and only if the set of characters on \(G\) is stable.
reviewed by: Do Ngoc Diep
Mathematics Subject Classification ID: 43A07
zbMATH DE Number: 1506534
zbMATH Keywords: pseudo-character
zbMATH Keywords: almost multiplicative functional
zbMATH Keywords: amenable locally compact group
zbMATH Keywords: Banach group algebra
MaRDI profile type: Publication
OpenAlex ID: W2102065240
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DOI: 10.1006/JMAA.2000.6898
description: scientific article; zbMATH DE number 1506534