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EQUILATERAL SETS IN UNIFORMLY SMOOTH BANACH SPACES

Part of:Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  02 January 2014

D. Freeman,
E. Odell,
B. Sari and
Th. Schlumprecht
D. Freeman
Affiliation:
Department of Mathematics and Computer Science, Saint Louis University, St Louis, MO 63103,U.S.A. email dfreema7@slu.edu
E. Odell
Affiliation:
Department of Mathematics, The University of Texas at Austin, Austin, TX 78712-0257,U.S.A. email odell@math.utexas.edu
B. Sari
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203-5017,U.S.A. email bunyamin@unt.edu
Th. Schlumprecht
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368,U.S.A. email schlump@math.tamu.edu

Abstract

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Let $X$ be an infinite-dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exist a constant $\lambda \gt 0$ and an infinite sequence $\mathop{({x}_{i} )}\nolimits_{i= 1}^{\infty } \subset X$ such that $\Vert {x}_{i} - {x}_{j} \Vert = \lambda $ for all $i\not = j$.

MSC classification

Secondary:46B20: Geometry and structure of normed linear spaces46B04: Isometric theory of Banach spaces

Information

Type
Research Article
Information
Mathematika , Volume 60 , Issue 1 , January 2014, pp. 219 - 231
Copyright
Copyright © University College London 2014 

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