JOHNSON AMENABILITY FOR TOPOLOGICAL SEMIGROUPS

A notion of amenability for topological semigroups is introduced. A topological semigroup S is called Johnson amenable if for every Banach S -bimodule E, every bounded crossed homomorphism from S to E* is principal. In this paper it is shown that a discrete semigroup S is Johnson amenable if and only if 1(S) is an amenable Banach algebra. Also, we show that if a topological semigroup S is Johnson amenable, then it is amenable, but the converse is not true.