A Hahn-Banach theorem for separation of semi-groups and its applications (Q582523)

The author studies a Hahn-Banach type theorem for separation of semigroups. For example, it is shown that if A, B are disjoint subsemigroups of an abelian semigroup S, that have nonempty algebraic cores, then there exists a real-valued homomorphism \(\mu\) on S such that \(\mu\) (a)\(\geq 0\geq \mu (b)\) for all \(a\in A\), \(b\in B\). This result is applied to obtain characterization theorems for semi-interval functions and separation theorems for semi-deviation means.