Extensions of Hamburger's Theorem

Stieltjes Perfect Semigroups are Perfect

“…equivalence relation containing R, and since ∼ is the least such equivalence relation, we infer that (12) (s)…”

“…But it is equal to µ r A * (G), which is positive. What we have just shown implies, by (7), that ϕ is a Stieltjes moment function. To see that it is Stieltjes determinate, it suffices to note that the semigroup S, being perfect, is determinate, hence trivially 'Stieltjes determinate'.…”

“…Every densely cosetlike semigroup is quasi-perfect [12]. It follows that a * -semigroup S is perfect if it is flat and (S) is densely cosetlike.…”

“…nx = y + z). If H is * -archimedean then every character on H is nowhere zero, so if H * separates points in H then H is cancellative [7]. A * -subsemigroup of a * -semigroup is a subsemigroup stable under the involution.…”

“…Thus µ s is concentrated on G s . By (12) we infer that for each u ∈ U there is a unique complex measure µ u on A 0 (S *…”