This is an announcement for the paper "Auerbach bases and minimal volume sufficient enlargements" by Mikhail 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 $P(B_Y)\subset A$. Each finite dimensional normed space has a minimal-volume sufficient enlargement which is a parallelepiped, some spaces have ``exotic'' minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having ``exotic'' minimal-volume sufficient enlargements in terms of Auerbach bases.

Archive classification: math.FA

Mathematics Subject Classification: 46B07 (primary), 52A21, 46B15 (secondary)

Submitted from: ostrovsm@stjohns.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1103.0997

or

http://arXiv.org/abs/1103.0997