Invertibility of multivalued sublinear operators

Abstract

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.