Linear selections for set-valued functions and extension of bilinear forms
The aim of this note is twofold. In the first part we give conditions on the extendability of bilinear functions defined on subspaces of a product space. The functions represented as the pointwise suprema of bilinear forms are also characterized. The second part deals with the extension of linear subselections of weakly compact convex set-valued mappings. A result of Rodriguez-Salinas and Bou states that such an extension of any linear subselection always exists if the set-valued map is sublinear and its values belong to a translation invariant family of subsets having the binary intersection property. Our aim is to formulate necessary and sufficient conditions that guarantee the existence of the extension for prescribed linear subselections.
extendability of bilinear functions defined on subspaces of a product space
extension of linear subselections of weakly compact convex set-valued mappings
scientific article; zbMATH DE number 590072