Sufficient enlargements of minimal volume for finite dimensional normed linear spaces
| dc.creator | Ostrovskii, M. I. | |
| dc.date | 2008-11-11 | |
| dc.date.accessioned | 2026-07-07T10:17:28Z | |
| dc.date.available | 2026-07-07T10:17:28Z | |
| dc.description | Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P:Y\to X$ such that $P(B_Y)\subset A$. The main results of the paper: {\bf (1)} Each minimal-volume sufficient enlargement is linearly equivalent to a zonotope spanned by multiples of columns of a totally unimodular matrix. {\bf (2)} If a finite dimensional normed linear space has a minimal-volume sufficient enlargement which is not a parallelepiped, then it contains a two-dimensional subspace whose unit ball is linearly equivalent to a regular hexagon. | |
| dc.identifier | https://arxiv.org/abs/0811.1701 | |
| dc.identifier | http://arxiv.org/abs/0811.1701 | |
| dc.identifier | J. Funct. Anal. 255 (2008), no. 3, 589-619 | |
| dc.identifier | doi:10.1016/j.jfa.2008.04.012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173864 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46B07, 52A21 | |
| dc.title | Sufficient enlargements of minimal volume for finite dimensional normed linear spaces | |
| dc.type | text |