Equilateral sets in infinite dimensional Banach spaces (Q2862184)
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scientific article; zbMATH DE number 6227017
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equilateral sets in infinite dimensional Banach spaces |
scientific article; zbMATH DE number 6227017 |
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Equilateral sets in infinite dimensional Banach spaces (English)
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14 November 2013
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equilateral set
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antipodal set
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biorthogonal system
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From the summary: ``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.''NEWLINENEWLINEA subset \(S\) of a metric space is equilateral if there exists a real \(\lambda> 0\) such that for \(x,y\in S\), if \(x\neq y\), then \(d(x,y)=\lambda\).
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