Universal spaces of subdifferentials of sublinear operators ranging in the cone of bounded lower semicontinuous functions

We study Fr,chet's problem of the universal space for the subdifferentials a,P of continuous sublinear operators P: V -> BC(X)(similar to) which are defined on separable Banach spaces V and range in the cone BC(X similar to f bounded lower semicontinuous functions on a normal topological space X. We prove that the space of linear compact operators L-c(l(2), C(beta X)) is universal in the topology of simple convergence. Here l(2) is a separable Hilbert space, and beta X is the Stone-Aech compactification of X. We show that the images of subdifferentials are also subdifferentials of sublinear operators.