When random proportional subspaces are also random quotients

Alexander E. Litvak, Vitali D. Milman, Nicole Tomczak-Jaegermann

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)270-289
Number of pages20
JournalJournal of Functional Analysis
Volume213
Issue number2
DOIs
StatePublished - 15 Aug 2004

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