  Banach algebra A for which the natural embedding x into x^ of A into WAP(A)*
is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||,
is called a WAP-algebra. Through we mainly concern with weighted measure
algebra M_b(S;w); where w is a weight on a semi-topological semigroup S. We
study those con- ditions under which M_b(S;w) is a WAP-algebra (respectively
dual Banach algebra). In particular, M_b(S) is a WAP-algebra (respectively dual
Banach algebra) if and only if wap(S) separates the points of S (respectively S
is compactly cancellative semigroup). We apply our results for improving some
older results in the case where S is discrete.
