Extensions of Hamburger's theorem (Q1281619)

The paper deals with some questions related to the generalizations of the classical Hamburger moment theorem concerning a finitely generated semigroup \(S\) with identical involution \(s^*=s\). The main result (Theorem 1) states that the semiperfectness and operator semiperfectness are equivalent, and both can be characterized in terms of of the structure of a certain homomorphic image of \(S\).