SOME PROPERTIES OF BOUNDED TRI-LINEAR MAPS

Let X, Y, Z and W be normed spaces and f : X x Y x Z -> W be a bounded tri-linear mapping. In this manuscript, we introduce the topological centers of bounded tri-linear mapping and we invistagate their properties. We study the relationships between weakly compactenss of bounded linear mappings and regularity of bounded tri-linear mappings. We extend some factorization property for bounded trilinear mappings. We also establish the relations between regularity and factorization property of bounded tri-linear mappings.