Multiplicative linear functionals in a commutative Banach algebra
type: Item
instance of: scholarly article
title: Multiplicative linear functionals in a commutative Banach algebra
zbMATH Open document ID: 0823.46052
DOI: 10.1007/BF01196583
author: Fariba Ershad
author: K. Seddighi
published in: Archiv der Mathematik
publication date: 1995-11-05T00:00:00Z
review text: Let \(\mathcal A\) be a commutative Banach algebra with identity. The Gleason- Kahane-Zelazko Theorem characterizes the multiplicative linear functionals on \(\mathcal A\). During the past fifteen years, several people have devoted their time to this part of functional analysis. Among them we can name B. Aupetit, S. Kowalski and Z. Slodkowski, K. Jarosz, C. R. Warner and R. Whitley, M. Roitman and Y. Sternfeld as well as G. Maltese. Maltese proved a special case of this theorem using the Minkowski- Carathéodory Theorem. R. Wille has done this using a measure theoretic argument. We present a simpler proof of this. We also prove a central theorem from which several results concerning the GKZ triples will easily follow. We also give some sufficient conditions on such algebras to have the \(P(k, n)\) property.
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 46J05
zbMATH DE Number: 779027
zbMATH Keywords: symmetric involution
zbMATH Keywords: positive functional
zbMATH Keywords: commutative Banach algebra with identity
zbMATH Keywords: Gleason-Kahane-Zelazko Theorem
zbMATH Keywords: multiplicative linear functionals
zbMATH Keywords: Minkowski-Carathéodory Theorem
zbMATH Keywords: GKZ triples
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 779027