Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in ln∞, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory