On locating isometric \(\ell_1^{(n)}\) (Q2764795)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On locating isometric \(\ell_1^{(n)}\) |
scientific article; zbMATH DE number 1690980
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On locating isometric \(\ell_1^{(n)}\) |
scientific article; zbMATH DE number 1690980 |
Statements
10 July 2003
0 references
normed space
0 references
hypercube
0 references
On locating isometric \(\ell_1^{(n)}\) (English)
0 references
Real normed spaces containing an isometric copy of \(\ell_1^{(n)}\) are characterized using the notion of a hypercube. An \(n\)-dimensional hypercube in a space \(X\) is a collection of \(2^n\) distinct vectors in \(X\) indexed by \(\{0,1\}^n\), the edges and diagonals are defined in the natural way. A space \(X\) contains a linear isometric copy of \(\ell_1^{(n)}\) if (and only if) it contains an \(n\)-dimensional hypercube such that the sum of the lengths of all edges is equal to the sum of the lengths of all diagonals.
0 references
