On the existence of dense ideals in \(LMC^*\)-algebras
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.
scientific article; zbMATH DE number 3967126