Linear selections for set-valued functions and extension of bilinear forms
type: Item
instance of: scholarly article
title: Linear selections for set-valued functions and extension of bilinear forms
zbMATH Open document ID: 0797.46005
DOI: 10.1007/BF01196433
author: Zsolt Páles
published in: Archiv der Mathematik
publication date: 1994-10-10T00:00:00Z
review text: 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.
reviewed by: Zsolt Páles
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 590072
zbMATH Keywords: extension of additive selections
zbMATH Keywords: Hahn-Banach theorem
zbMATH Keywords: extendability of bilinear functions defined on subspaces of a product space
zbMATH Keywords: pointwise suprema of bilinear forms
zbMATH Keywords: extension of linear subselections of weakly compact convex set-valued mappings
MaRDI profile type: Publication
cites work: Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings
full work available at URL: https://doi.org/10.1007/bf01196433
OpenAlex ID: W2018119054
description: scientific article; zbMATH DE number 590072