Random Euclidean sections of some classical Banach spaces

  • Y. Gordon
  • O. Guédon
  • M. Meyer
  • A. Pajor

Abstract

Using probabilistic arguments, we give precise estimates of the Banach-Mazur distance of subspaces of the classical $\ell_q^n$ spaces and of Schatten classes of operators $S_q^n$ for $q \ge 2$ to the Euclidean space. We also estimate volume ratios of random subspaces of a normed space with respect to subspaces of quotients of $\ell_q$. Finally, the preceeding methods are applied to give estimates of Gelfand numbers of some linear operators.
Published
2002-12-01
How to Cite
Gordon, Y., Guédon, O., Meyer, M., & Pajor, A. (2002). Random Euclidean sections of some classical Banach spaces. MATHEMATICA SCANDINAVICA, 91(2), 247-268. https://doi.org/10.7146/math.scand.a-14389
Section
Articles