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

Árpád Száz

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 3, page 235-249
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Árpád Száz. "The intersection convolution of relations and the Hahn-Banach type theorems." Annales Polonici Mathematici 69.3 (1998): 235-249. <http://eudml.org/doc/270701>.

@article{ÁrpádSzáz1998,
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.},
author = {Árpád Száz},
journal = {Annales Polonici Mathematici},
keywords = {intersection convolution; additive and homogeneous relations; linear selections; binary intersection property; Hahn-Banach theorems; Hahn-Banach extension theorem; injectivity of Banach spaces; Hausdorff's maximality principle; Nachbin's Theorem},
language = {eng},
number = {3},
pages = {235-249},
title = {The intersection convolution of relations and the Hahn-Banach type theorems},
url = {http://eudml.org/doc/270701},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Árpád Száz
TI - The intersection convolution of relations and the Hahn-Banach type theorems
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 3
SP - 235
EP - 249
AB - 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.
LA - eng
KW - intersection convolution; additive and homogeneous relations; linear selections; binary intersection property; Hahn-Banach theorems; Hahn-Banach extension theorem; injectivity of Banach spaces; Hausdorff's maximality principle; Nachbin's Theorem
UR - http://eudml.org/doc/270701
ER -

References

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