Representation of the compact-valued sublinear operator by basis selectors packet and sub-invertibility

We consider two close ways of linearization for sublinear operator that takes compact convex values. The first way consists in a representation of given multioperator by the family of so called basis selectors that are single-valued linear bounded operators. The second way consists in linear extension of given multioperator from its values on some Hamel basis. Every of the ways above leads to its own concept of subinvertibility for the initial multioperator.