Auerbach Bases and Minimal Volume Sufficient Enlargements

Canadian mathematical bulletin

M. I. Ostrovskii¹ 

[1] Department of Mathematics and Computer Science, St. John's University, Queens, NY 11439, U.S.A.

关键词: Banach space;    Auerbach basis;    sufficient enlargement;   

DOI  :  10.4153/CMB-2011-043-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $B_Y$ denote the unit ball of anormed linear space $Y$. A symmetric, bounded, closed, convex set$A$ in a finite dimensional normed linear space $X$ is called asufficient enlargement for $X$ if, for an arbitraryisometric embedding of $X$ into a Banach space $Y$, there exists alinear projection $Pcolon Yo X$ such that $P(B_Y)subset A$. Eachfinite dimensional normed space has a minimal-volume sufficientenlargement that is a parallelepiped; some spaces have ``exotic''minimal-volume sufficient enlargements. The main result of thepaper is a characterization of spaces having ``exotic''minimal-volume sufficient enlargements in terms of Auerbachbases.

【 授权许可】

Unknown