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 | ||||||
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| 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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