Equilateral sets in infinite dimensional Banach spaces

Mercourakis, S.; Vassiliadis, G.

doi:10.1090/S0002-9939-2013-11746-6

Equilateral sets in infinite dimensional Banach spaces
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by S. K. Mercourakis and G. Vassiliadis PDF

Proc. Amer. Math. Soc. 142 (2014), 205-212 Request permission

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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