1. CMB 2011 (vol 54 pp. 726)
|Auerbach Bases and Minimal Volume Sufficient Enlargements|
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 sufficient enlargement for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P\colon Y\to X$ such that $P(B_Y)\subset A$. Each finite dimensional normed space has a minimal-volume sufficient enlargement that 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.
Keywords:Banach space, Auerbach basis, sufficient enlargement
Categories:46B07, 52A21, 46B15