This is an announcement for the paper "Sufficient enlargements of minimal volume for finite dimensional normed linear spaces" by M.I. Ostrovskii.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B07, 52A21

Citation: J. Funct. Anal. 255 (2008), no. 3, 589-619

The source file(s), ost.tex: 97543 bytes, is(are) stored in gzipped form as 0811.1701.gz with size 28kb. The corresponding postcript file has gzipped size 173kb.

Submitted from: ostrovsm@stjohns.edu

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