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

Annales Polonici Mathematici (1998)

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

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topÁrpád 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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