Asymptotic expression of the linear discrete best lp-approximation

Let h(p), 1 < p < infinity, be the best l(p)-approximation of the element h is an element of R-n from a proper affine subspace K of R-n, h is not an element of K, and let h(infinity)* denote the strict uniform approximation of h from K. We prove that there are a vector alpha is an element of R-n\{0} and a real number a, 0 <= a <= 1, such that h(p) = h(infinity)* + a(p)/p-1 alpha + gamma(p), for all p > 1, where gamma(p) is an element of R-n with parallel to gamma(p)parallel to = o (a(p) / p). (C) 2006 Elsevier Inc. All rights reserved.