Extremely amenable transformation semigroups, II
Kôskichi Sakai · Proceedings of the Japan Academy Series A Mathematical Sciences · 1974
Introduction.Let S be a semigroup and X a nonvoid set.Then we shall say that the pair (S, X) is a transformation semigroup if for every s e S there corresponds a map" X xsx e X such that s(tx) ----(st)x for all s, t in S and x in X.Let B(X) be the Banach algebra of all real valued bounded functions on X with the supremum norm and B(X)* the conjugate Banach space of B(X).For every s e S de- fine the map L" B(X)-B(X) by L,f=sf for f e B(X), where f(x) =f(sx) for x in X.Then we have LLt=Lts and L [_1 for all s, t in S. The map L" sL, is called the left regular antirepresentation of