Asymptotic expression of the linear discrete best ℓp-approximation

AbstractLet hp, 1<p<∞, be the best ℓp-approximation of the element h∈Rn from a proper affine subspace K of Rn, h∉K, and let h∞* denote the strict uniform approximation of h from K. We prove that there are a vector α∈Rn⧹{0} and a real number a, 0⩽a⩽1, such thathp=h∞*+app-1α+γp,for all p>1, where γp∈Rn with ∥γp∥=oap/p