Verwandte Operatoren.
There exists an absolute constant such that for any n-dimensional Banach space E there exists a k-dimensional subspace F ⊂ E with k≤ n/2 such that . The concept of volume ratio with respect to -spaces is used to prove the following distance estimate for : .
The geometry of random projections of centrally symmetric convex bodies in is studied. It is shown that if for such a body K the Euclidean ball is the ellipsoid of minimal volume containing it and a random n-dimensional projection is “far” from then the (random) body B is as “rigid” as its “distance” to permits. The result holds for the full range of dimensions 1 ≤ n ≤ λN, for arbitrary λ ∈ (0,1).