Hyperplane projections of the unit ball of l(p)(n)
Abstract
Let B-p(n) = {x is an element of R-n; Sigma(i=1)(n) \x(i)\(p) less than or equal to 1}, 1 less than or equal to p less than or equal to +infinity. We study the extreme values of the volume of the orthogonal projection of B-p(n) onto hyperplanes H subset of R-n. For a fixed H, we prove that the ratio vol(PHBpn)/vol(B-p(n-1)) is non-decreasing in p is an element of [1, +infinity].