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.

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DOI: http://dx.doi.org/10.7146/math.scand.a-14389

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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