On the existence of dense ideals in \(LMC^*\)-algebras
type: Item
instance of: scholarly article
title: On the existence of dense ideals in \(LMC^*\)-algebras
zbMATH Open document ID: 0599.46076
DOI: 10.4171/ZAA/21
author: M. Fritzsche
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1982-01-01T00:00:00Z
review text: An \(LMC^*\)-algebra is a complete locally convex algebra A whose topology can be given by means of a family \(\{p_{\alpha}\}\) of submultiplicative seminorms satisfying \(p_{\alpha}(x^*x)=p_{\alpha}(x)^ 2\) for all x in A and all indices \(\alpha\). An element x in A is said to be unbounded if \(\sup_{\alpha}p_{\alpha}(x)=\infty\). The main result of the paper states that if an \(LMC^*\)-algebra with unit has an unbounded element then it also has a dense one-sided ideal.
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 46H10
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3967126
zbMATH Keywords: \(LMC^*\)-algebra
zbMATH Keywords: submultiplicative seminorms
zbMATH Keywords: unbounded element
zbMATH Keywords: dense one-sided ideal
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3967126