Auerbach bases and minimal volume sufficient enlargements
نویسنده
چکیده
Let BY 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 : Y → X such that P (BY ) ⊂ 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. 2000 Mathematics Subject Classification: 46B07 (primary), 52A21, 46B15 (secondary).
منابع مشابه
2 00 2 Projections in Normed Linear Spaces and Sufficient Enlargements
Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists a projection P : Y → X such that P (B(Y)) ⊂ A (by B we denote the unit ball). The main purpose of the present paper is to continue investigation of sufficien...
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