Some remarks on spectral states of LMC-algebras
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.
spectral state on a unital Banach algebra
integral representations of spectral states
scientific article; zbMATH DE number 4165727
scientific article