On the nontrivial projection problem

Details On the nontrivial projection problem On the nontrivial projection problem

2008-05-24

arxiv.org/abs/0805.3792v1

Advances In Math. 221 (2009), 331-342

Mathematics

Functional Analysis

17 pages

Scientific paper

10.1016/j.aim.2008.12.004

The Nontrivial Projection Problem asks whether every finite-dimensional normed space of dimension greater than one admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension greater than one) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true "up to a logarithmic factor."

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