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On the nontrivial projection problem |
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| Authors: | Stanislaw J. Szarek Nicole Tomczak-Jaegermann |
| Affiliation: | a Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106-7058, USA b Equipe d'Analyse Fonctionnelle, BP 186, Université Pierre et Marie Curie, 75252 Paris, France c Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 |
| Abstract: | The nontrivial projection problem asks whether every finite-dimensional normed space admits a well-bounded projection of nontrivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension) is approximately affinely equivalent to a direct product of two bodies of nontrivial dimensions. We show that this is true “up to a logarithmic factor.” |
| Keywords: | primary, 46B20 secondary, 46B07, 52A21 |
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