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Equilateral sets in infinite dimensional Banach spaces


Authors: S. K. Mercourakis and G. Vassiliadis
Journal: Proc. Amer. Math. Soc. 142 (2014), 205-212
MSC (2010): Primary 46B20; Secondary 46B06, 46B04
Published electronically: September 20, 2013
MathSciNet review: 3119196
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Abstract: We show that every Banach space $ X$ containing an isomorphic copy of $ c_0$ has an infinite equilateral set and also that if $ X$ has a bounded biorthogonal system of size $ \alpha $, then it can be renormed so as to admit an equilateral set of equal size.


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Additional Information

S. K. Mercourakis
Affiliation: Department of Mathematics, University of Athens, 15784 Athens, Greece
Email: smercour@math.uoa.gr

G. Vassiliadis
Affiliation: Department of Mathematics, University of Athens, 15784 Athens, Greece
Email: georgevassil@hotmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11746-6
Keywords: Equilateral set, antipodal set, biorthogonal system.
Received by editor(s): November 28, 2011
Received by editor(s) in revised form: December 23, 2011, February 24, 2012, and February 29, 2012
Published electronically: September 20, 2013
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.