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On Locating Isometric $\ell_{1}^{(n)}$

  Published:2001-09-01
 Printed: Sep 2001
  • Anthony Weston
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Abstract

Motivated by a question of Per Enflo, we develop a hypercube criterion for locating linear isometric copies of $\lone$ in an arbitrary real normed space $X$. The said criterion involves finding $2^{n}$ points in $X$ that satisfy one metric equality. This contrasts nicely to the standard classical criterion wherein one seeks $n$ points that satisfy $2^{n-1}$ metric equalities.
Keywords: normed spaces, hypercubes normed spaces, hypercubes
MSC Classifications: 46B04, 05C10, 05B99 show english descriptions Isometric theory of Banach spaces
Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
None of the above, but in this section
46B04 - Isometric theory of Banach spaces
05C10 - Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
05B99 - None of the above, but in this section
 

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