[Banach] Abstract of a paper by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner

This is an announcement for the paper "Dual affine invariant points" by Mathieu Meyer, Carsten Schuett, and Elisabeth M. Werner.

Abstract: An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations A on R^n, that is, p(A(K))=A(p(K)). We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K^{p(K)})=p(K) for every convex body K, where K^{p(K)} denotes the polar of K with respect to p(K). We investigate which affine invariant points do have a dual point, whether this dual point is unique and has itself a dual point. We define a product on the set of affine invariant points, in relation with duality. Finally, examples are given which exhibit the rich structure of the set of affine invariant points.

Archive classification: math.FA

Submitted from: elisabeth.werner@case.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1310.0128

or

http://arXiv.org/abs/1310.0128