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Choice free fixed point property in separable Banach spaces


Author: Vassilios Gregoriades
Journal: Proc. Amer. Math. Soc. 143 (2015), 2143-2157
MSC (2010): Primary 47H10, 03E15, 54H05, 54H25
DOI: https://doi.org/10.1090/S0002-9939-2015-12465-3
Published electronically: January 8, 2015
MathSciNet review: 3314122
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Abstract: We show that the standard approach of minimal invariant sets, which applies Zorn's Lemma and is used to prove fixed point theorems for non-expansive mappings in Banach spaces, can be applied without any reference to the full Axiom of Choice when the given Banach space is separable. Our method applies results from classical and effective descriptive set theory.


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Additional Information

Vassilios Gregoriades
Affiliation: Technische Universität Darmstadt, Fachbereich Mathematik, Arbeitsgruppe Logik, Schloßgartenstraße 7, 64289 Darmstadt, Germany
Email: gregoriades@mathematik.tu-darmstadt.de

DOI: https://doi.org/10.1090/S0002-9939-2015-12465-3
Keywords: Minimal invariant sets, non-expansive mappings, fixed point property, Axiom of Choice, effective descriptive set theory.
Received by editor(s): May 8, 2013
Received by editor(s) in revised form: November 5, 2013
Published electronically: January 8, 2015
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2015 American Mathematical Society