Special orthogonal splittings of $L_1^{2k}$

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dc.creatorSchechtman, Gideon
dc.date2003-01-24
dc.date2003-03-09
dc.date.accessioned2026-07-07T04:54:39Z
dc.date.available2026-07-07T04:54:39Z
dc.descriptionWe show that for each positive integer $k$ there is a $k\times k$ matrix $B$ with $\pm 1$ entries such that putting $E$ to be the span of the rows of the $k\times 2k$ matrix $[\sqrt{k}I_k,B]$, then $E,E^{\bot}$ is a Kashin splitting: The $L_1^{2k}$ and the $L_2^{2k}$ are universally equivalent on both $E$ and $E^{\bot}$. Moreover, the probability that a random $\pm 1$ matrix satisfies the above is exponentially close to 1.
dc.descriptionSome minor corrections
dc.identifierhttps://arxiv.org/abs/math/0301275
dc.identifierhttp://arxiv.org/abs/math/0301275
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66342
dc.subjectFunctional Analysis
dc.subjectProbability
dc.subject46B07
dc.titleSpecial orthogonal splittings of $L_1^{2k}$
dc.typetext

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