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Linear Hahn–Banach extension operators

Published online by Cambridge University Press:  20 January 2009

Brailey Sims  and
David Yost
Brailey Sims
Affiliation:
Department of Mathematics, Statistics and Computing ScienceUniversity of New EnglandArmidaleN.S.W. 2351Australia
David Yost
Affiliation:
Department of MathematicsInstitute of Advanced StudiesAustralian National UniversityG.P.O. Box 4A.C.T. 2601Australia
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Given any subspace N of a Banach space X, there is a subspace M containing N and of the same density character as N, for which there exists a linear Hahn–Banach extension operator from M* to X*. This result was first proved by Heinrich and Mankiewicz [4, Proposition 3.4] using some of the deeper results of Model Theory. More precisely, they used the Banach space version of the Löwenheim–Skolem theorem due to Stern [11], which in turn relies on the Löwenheim–Skolem and Keisler–Shelah theorems from Model Theory. Previously Lindenstrauss [7], using a finite dimensional lemma and a compactness argument, obtained a version of this for reflexive spaces. We shall show that the same finite dimensional lemma leads directly to the general result, without any appeal to Model Theory.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 53 - 57
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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