Remarks on the geometry of coordinate projections in R^n

Details Remarks on the geometry of coordinate projections in R^n Remarks on the geometry of coordinate projections in R^n

2003-06-22

arxiv.org/abs/math/0306314v1

Mathematics

Functional Analysis

Israel Journal of Mathematics, to appear

Scientific paper

We study geometric properties of coordinate projections. Among other results, we show that if a body K in R^n has an "almost extremal" volume ratio, then it has a projection of proportional dimension which is close to the cube. We compare type 2 and infratype 2 constant of a Banach space. This follows from a comparison lemma for Rademacher and Gaussian averages. We also establish a sharp estimate on the shattering dimension of the convex hull of a class of functions in terms of the shattering dimension of the class itself.

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