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Some extensions of a dual of the Hahn-Banach Theorem, with applications to separation and Helly type theorems

Published online by Cambridge University Press:  17 April 2009

Ivan Singer
Ivan Singer
Affiliation:
Institute of Mathematics, Bucureşti, Romania; National Institute for Scientific and Technical Creation, Bucureşti, Romania.
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Abstract

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In previous papers we have proved that if G is a ω*-closed subspace of the conjugate space B* of a normed linear space B, then every b ∈ B can be extended within B, from G to the whole B*, with an arbitrarily small increase of the norm. Here we give some extensions of this result to the case when B* is replaced by a normed linear space E and B by any linear subspace V of E*, and some applications to separation and Helly type theorems.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 2 , October 1976 , pp. 277 - 291
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Alfsen, Erik M. and Effros, Edward G., “Structure in real Banach spaces. Part I”, Ann. of Math. (2) 96 (1972), 98–128.CrossRefGoogle Scholar
[2]Banach, Stefan, Théorie des opérations linéaires (Monografje Matematyczne, I. Subwencji Funduszu Kultury Narodowej, Warszawa, 1932).Google Scholar
[3]Day, Mahlon M., Normed linear spaces, 3rd ed. (Ergebnisse der Mathematik und ihrer Grenzgebiete, 21. Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[4]Dixmier, J., “Sur un théeorème de Banach”, Duke Math. J. 15 (1918), 1057–1071.Google Scholar
[5]Dunford, Nelson and Schwartz, Jacob J., Linear operators. Part I: General theory (Pure and Applied Mathematics, 7. Interscience, New York, London, 1958).Google Scholar
[6]Günzler, H., “Über ein Analogon zum Satz von Hahn und Banach”, Arch. Math. (Basel) 10 (1959), 366–372.CrossRefGoogle Scholar
[7]Singer, Ivan, “Un dual du théorème de Hahn-Banach”, C.R. Acad. Sci. Paris Sér. A 247 (1958), 408–411.Google Scholar
[8]Singer, Ivan, “Quelques applications d'un dual du théorème de Hahn-Banach”, C.R. Acad. Sci. Paris Sér. A 247 (1958), 846–849.Google Scholar
[9]Singer, Ivan, “Sur un dual du théorème de Hahn-Banach et sur un théorème de Banach”, Rend. Accad. Naz. Lincei 25 (1958), 443–446.Google Scholar