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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.

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

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