Hewitt-Zuckerman semigroups in the structure semigroups of measure algebras

Abstract

Let 9~ be a semisimple commutative measure algebra with an identity of norm one. It is well known, due to Taylor [5], that there is a compact abelian semigroup S with identity, called the structure semigroup of 99l, and an order preserving i somorphismisomet ry /~ /~ of 93l onto a weak* dense subalgebra Ms(S ) of M(S). Furthermore, each complex homomorphism of 9J~ is determined by a unique semicharacter f e S through the pairing