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.
@article{bwmeta1.element.bwnjournal-article-apmv69z3p235bwm,
author = {\'Arp\'ad Sz\'az},
title = {The intersection convolution of relations and the Hahn-Banach type theorems},
journal = {Annales Polonici Mathematici},
volume = {69},
year = {1998},
pages = {235-249},
zbl = {0929.46004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z3p235bwm}
}
Árpád Száz. The intersection convolution of relations and the Hahn-Banach type theorems. Annales Polonici Mathematici, Tome 69 (1998) pp. 235-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z3p235bwm/
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