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Special orthogonal splittings ofL 2k1

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Abstract

We show that for each positive integerk there is ak×k matrixB with ±1 entries such that puttingE to be the span of the rows of thek×2k matrix [√kI k,B], thenE,E ⊥ is a Kashin splitting: TheL 2k1 and theL 2k2 are universally equivalent on bothE andE ⊥. Moreover, the probability that a random ±1 matrix satisfies the above is exponentially close to 1.

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Authors and Affiliations

  1. Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Gideon Schechtman

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  1. Gideon Schechtman
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Correspondence to Gideon Schechtman.

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Supported by the Israel Science Foundation.

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Schechtman, G. Special orthogonal splittings ofL 2k1 . Isr. J. Math. 139, 337–347 (2004). https://doi.org/10.1007/BF02787555

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  • DOI: https://doi.org/10.1007/BF02787555

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