ON THE EXISTENCE OF 1-SEPARATED SEQUENCES ON THE UNIT BALL OF A FINITE-DIMENSIONAL BANACH SPACE

Given a finite-dimensional Banach space $X$ and an Auerbach basis $\{(x_{k},x_{k}^{\ast }):1\leqslant k\leqslant n\}$ of $X$, it is proved that there exist $n+1$ linear combinations $z_{1},\ldots ,z_{n+1}$ of $x_{1},\ldots ,x_{n}$ with coordinates $0,\pm 1$, such that $\Vert z_{k}\Vert =1$, for $k=1...

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Veröffentlicht in:	Mathematika 2015-09, Vol.61 (3), p.547-558, Article 547
Hauptverfasser:	Glakousakis, E., Mercourakis, S.
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Sprache:	eng
Schlagworte:	46B20 52A21 (primary) 52C99 (secondary)
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description	Given a finite-dimensional Banach space $X$ and an Auerbach basis $\{(x_{k},x_{k}^{\ast }):1\leqslant k\leqslant n\}$ of $X$, it is proved that there exist $n+1$ linear combinations $z_{1},\ldots ,z_{n+1}$ of $x_{1},\ldots ,x_{n}$ with coordinates $0,\pm 1$, such that $\Vert z_{k}\Vert =1$, for $k=1$, $2,\ldots ,n+1$ and $\Vert z_{k}-z_{l}\Vert >1$, for $1\leqslant k
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title	ON THE EXISTENCE OF 1-SEPARATED SEQUENCES ON THE UNIT BALL OF A FINITE-DIMENSIONAL BANACH SPACE
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