Quasi-interior Points and the Extension of Linear Functionals View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1966

AUTHORS

R. E. Fullerton , C. C. Braunschweiger

ABSTRACT

Let X be a real normed space, M a linear subspace of X, and X’ and M’ the spaces conjugate to X and M, respectively. It is known from the Hahn-Banach theorem [2] that to each f in M’ there corresponds at least one x’ in X’ with the same norm such that x’ (x) = f(x) for each x in M. The question of when this norm preserving extension is unique has received considerable attention. Taylor [15] and Foguel [4] have shown that this extension is unique for every subspace M of X and for each f in M’ if and only if the unit ball in X’ is strictly convex. Phelps [12] has shown that each f in M’ has a unique norm preserving extension in X’ if and only if the annihilator M┴ of M has the Haar property in X’; that is, if and only if to each x’ in X’ corresponds a unique y’ in M┴ such that ||x’, − y’|| = inf {||x’ − z’||: z’ ϵ M ┴}. More... »

PAGES

214-224

Book

TITLE

Contributions to Functional Analysis

ISBN

978-3-642-85999-1
978-3-642-85997-7

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-85997-7_11

DOI

http://dx.doi.org/10.1007/978-3-642-85997-7_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047112755


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