On the relation between the scalar moment problem and the matrix moment problem on *-semigroups
The author presents an example of a commutative \(*\)-semigroup with identity which is semiperfect of order~\(1\) but not of order~\(2\). Here, a commutative \(*\)-semigroup \(S\) is called semiperfect of order \(d\) (where \(d\) is a positive integer) if every matrix-valued function \(f: S\to M_d({\mathbb C})\) of positive type is of the form \(f(s)=\int_{S^*}\sigma(s)\, d\mu(\sigma)\) for some \(M_d({\mathbb C})_+\)-valued measure~\(\mu\) on the space \(S^*\) of characters of~\(S\) (i.e., non-zero, hermitian, multiplicative functions on~\(S\)).
scientific article; zbMATH DE number 2077983