Multiplicative linear functionals in a commutative Banach algebra
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.
commutative Banach algebra with identity
scientific article; zbMATH DE number 779027
scientific article