Products of Vector Measures

We consider the problem of the existence of the product of two vector measures with respect to a continuous bilinear map. We study conditions on the linear map induced by the bilinear form in order to assure the existence of the product of any two vector measures with respect to it. We show that every measure with values in lp admits product with any measure with values in lq with respect to any continuous bilinear map defined on lp=lq if and only if p, qgw1, 2x and min p, q4s1. We also show that there exist measures that admit product with any vector measure with respect to a fixed bilinear map although their semivariations in the sense of Bartle do not have a control measure