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A converse to the Eidelheit theorem in real Hilbert spaces |
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| Authors: | Emil Ernst Michel Théra |
| Institution: | a Laboratoire de Modélisation en Mécanique et Thermodynamique, Faculté de Sciences et Techniques de Saint Jérôme, Casse 322, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France b LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges Cedex, France |
| Abstract: | We establish the following converse to the Eidelheit theorem: an unbounded closed and convex set of a real Hilbert space may be separated by a closed hyperplane from every other disjoint closed and convex set, if and only if it has a finite codimension and a non-empty interior with respect to its affine hull. |
| Keywords: | Convex separation Hahn-Banach theorem Eidelheit theorem Compactly epi-lipschitzian sets |
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