When random proportional subspaces are also random quotients

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• 作者：Litvak ; Alexander E. ; Milman ; Vitali D. ; Tomczak-Jaegermann ; Nicole
• 刊名：Journal of Functional Analysis
• 出版年：2004
• 出版时间：August 15, 2004
• 年：2004
• 卷：213
• 期：2
• 页码：270-289
• 全文大小：301 K

文摘

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.