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Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem

Luxemburg, W. A. J. and Väth, Martin (2001) Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem. Zeitschrift für Analysis und ihre Anwendungen, 20 (2). pp. 267-279. ISSN 0232-2064. https://resolver.caltech.edu/CaltechAUTHORS:20181003-135833363

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Abstract

We show that it is impossible to prove the existence of a linear (bounded or unbounded) functional on any L_∞/C_0 without an uncountable form of the axiom of choice. Moreover, we show that if on each Banach space there exists at least one non-trivial bounded linear functional, then the Hahn-Banach extension theorem must hold. We also discuss relations of non-measurable sets and the Hahn-Banach extension theorem.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.4171/zaa/1015DOIArticle
Additional Information:© 2001 EMS Publishing House.
Subject Keywords:Power of the Hahn-Banach theorem, linear functionals, axiom of choice, axiom of dependent choices, Shelah’s model
Issue or Number:2
Record Number:CaltechAUTHORS:20181003-135833363
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181003-135833363
Official Citation:Luxemburg W.A.J., Väth Martin: The Existence of Non-Trivial Bounded Functionals Implies the Hahn-Banach Extension Theorem. Z. Anal. Anwend. 20 (2001), 267-279. doi: 10.4171/ZAA/1015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90099
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Oct 2018 23:35
Last Modified:03 Oct 2019 20:22

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