Invertibility of multivalued sublinear operators

We consider the representation of a compact-valued sublinear operator ($K$-operator) by means of the compact convex packet of single-valued so-called basis selectors. Such representation makes it possible to introduce the concept of an invertible $K$-operator via invertible selectors. The extremal points of direct and inverse selector representations are described, an analogue of the von Neumann theorem is obtained. A series of examples is considered.