A NECESSARY AND SUFFICIENT CONDITION FOR M(X) TO BE A SEMIGROUP WHERE X IS A SUBSPACE OF L1(R+; 1

In this paper, we have shown that, if X is a subspace of L1(R+; 1 w) which is closed under complex conjugation and containing w, is not necessarily a semigroup, where R+ = [0;1). In fact, we have given a necessary and sufficient condition for M(X) to be a semigroup with respect to the Arens multiplication