Ben, John's theorem is easier for unit balls of spaces which have a one symmetric basis because you can argue that the basis vectors must be orthogonal with respect to the Euclidean norm determined by the maximal volume ellipsoid and all the basis vectors must have the same Euclidean norm. At UMich you have two of the a top experts expert in this direction (Rudelson & Vershynin); Vershynin); talk to themhim.
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Ben, John's theorem is easier for unit balls of spaces which have a one symmetric basis because you can argue that the basis vectors must be orthogonal with respect to the Euclidean norm determined by the maximal volume ellipsoid and all the basis vectors must have the same Euclidean norm. At UMich you have two of the top experts in this direction (Rudelson & Vershynin); talk to them. |
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