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Title

The intersection convolution of relations and the Hahn-Banach type theorems

Authors 1

Affiliations

  1. Institute of Mathematics and Informatics, Lajos Kossuth University, H-4010 Debrecen, Pf. 12, Hungary

Abstract

By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an extension to a total linear selection.

Keywords

ENG
intersection convolution, additive and homogeneous relations, linear selections, binary intersection property, Hahn-Banach theorems

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Annales Polonici Mathematici
1998/69/3
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Pages:
235-249
Main language of publication
English
Received
1997-07-17
Accepted
1998-03-12
Published
1998
Exact and natural sciences