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Restricted invertibility and the Banach-Mazur distance to the cube

Abstract : We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate. As a consequence, we also recover the best known estimate for the Banach-Mazur distance to the cube: the distance of every n-dimensional normed space from \ell_{\infty}^n is at most (2n)^(5/6). Finally, using tools from the work of Batson-Spielman-Srivastava, we give a new proof for a theorem of Kashin-Tzafriri on the norm of restricted matrices.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00811793
Contributor : Pierre Youssef <>
Submitted on : Thursday, April 11, 2013 - 10:25:31 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM
Long-term archiving on: : Monday, April 3, 2017 - 4:04:01 AM

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Pierre Youssef. Restricted invertibility and the Banach-Mazur distance to the cube. 2012. ⟨hal-00811793⟩

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