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On the Hahn-Banach Extension Property

Published online by Cambridge University Press:  20 November 2018

Ting-On To
Ting-On To*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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In this paper, we consider real linear spaces. By (V:‖ ‖) we mean a normed (real) linear space V with norm ‖ ‖. By the statement "V has the (Y, X) norm preserving (Hahn-Banach) extension property" we mean the following: Y is a subspace of the normed linear space X, V is a normed linear space, and any bounded linear function f: Y → V has a linear extension F: X → V such that ‖F‖ = ‖f‖. By the statement "V has the unrestricted norm preserving (Hahn-Banach) extension property" we mean that V has the (Y, X) norm preserving extension property for all Y and X with Y ⊂ X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 9 - 13
Copyright
Copyright © Canadian Mathematical Society 1970

References

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