some results in the topological centers of module actions

Let be a banach and let zb(a) and za(b) be the topological centers of the left module action pi: a*b-b and the right module action pi:b*a- b , respectively. we investigate the relationships between topological center of a, z1(a) , with respect to the first arens product and topological centers of module actions zb(a) and za(b). on the other hand, if a has mazure property and b has the left a** factorization za**(b)=b , , then . for a locally compact noncompact group g with compact covering number card (g) we have z(l^1(g**))=l^1(g**) and z(m(g)**)=m(g).