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Maximal \(\ell_p^n\)-Structures in Spaces with Extremal Parameters

  • G. SchechtmanEmail author
  • N. Tomczak-Jaegermann
  • R. Vershynin
Chapter
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Part of the Lecture Notes in Mathematics book series (LNM, volume 1807)

Abstract

We prove that every n-dimensional normed space with a type p < 2, cotype 2, and (asymptotically) extremal Euclidean distance has a quotient of a subspace, which is well isomorphic to \(\ell_p^k\) and with the dimension k almost proportional to n. A structural result of a similar nature is also proved for a sequence of vectors with extremal Rademacher average inside a space of type p. The proofs are based on new results on restricted invertibility of operators from \(\ell_r^n\) into a normed space X with either type r or cotype r.

Mathematics Subject Classification (2000):

46-06 46B07 52-06 60-06 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • G. Schechtman
    • 1
    Email author
  • N. Tomczak-Jaegermann
    • 2
  • R. Vershynin
    • 1
    • 2
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Department of Mathematical SciencesUniversity of AlbertaEdmontonCanada

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