Some remarks on spectral states of LMC-algebras
type: Item
instance of: scholarly article
title: Some remarks on spectral states of LMC-algebras
zbMATH Open document ID: 0709.46029
DOI: 10.1007/BF02862879
author: Michael Pannenberg
publication date: 1990-01-01T00:00:00Z
review text: A spectral state on a unital Banach algebra A is a linear functional \(\phi\) satisfying \(\phi (1)=1\) and \(| \phi (x)| \leq \| x\|_{\sigma}\) for all x in A. The concept of spectral state in a complex unital locally multiplicatively convex algebra B is introduced in this article by using the above definition and by embedding B densely in a projective limit of Banach algebras. The author obtains integral representations of spectral states, determines their complex extreme points (in the commutative case) and discusses a wide variety of other topics - symmetric involutions, positive states, weak\({}^*\)-boundedness of the set of all spectral states, Korovkin-type theorems and commutativity criteria.
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 4165727
zbMATH Keywords: spectral state on a unital Banach algebra
zbMATH Keywords: locally multiplicatively convex algebra
zbMATH Keywords: integral representations of spectral states
zbMATH Keywords: complex extreme points
zbMATH Keywords: symmetric involutions
zbMATH Keywords: positive states
zbMATH Keywords: \(weak^ *\)- boundedness
zbMATH Keywords: Korovkin-type theorems
zbMATH Keywords: commutativity criteria
reviewed by: Seán Dineen
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4165727