Canadian mathematical bulletin | |
Auerbach Bases and Minimal Volume Sufficient Enlargements | |
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
【 预 览 】
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