Isomorphic random subspaces and quotients of convex and quasi-convex bodies

Abstract

We extend the results of [LMT] to the non-symmetric and quasiconvex cases. Namely, we consider finite-dimensional space endowed with gauge of either closed convex body (not necessarily symmetric) or closed symmetric quasi-convex body. We show that if a generic subspace of some fixed proportional dimension of one such space is isomorphic to a generic quotient of some proportional dimension of another space then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.

Cite this paper

@inproceedings{Litvak2004IsomorphicRS, title={Isomorphic random subspaces and quotients of convex and quasi-convex bodies}, author={Alexander E. Litvak and V. D. Milman and Nicole Tomczak-Jaegermann}, year={2004} }