Abstract
We consider the problem of extending or factorizing a bounded bilinear map defined on a couple of order continuous Banach function spaces to its optimal domain, i.e. the biggest couple of Banach function spaces to which the bilinear map can be extended. As in the case of linear operators, we use vector measure techniques to find this space, and
we show that this procedure cannot be always successfully used for bilinear maps. We also
present some applications to find optimal factorizations of linear operators between Banach
function spaces.
