2026/08/05 by Mario Ullrich
Mathematics · #math.FA #math.OA #math.SP
18 pages
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We prove an(S) ≤ e (n+1) sn(S) for every s-number sequence (sn), every bounded linear operator S between normed spaces, and every n ∈ ℕ0, where an are the approximation numbers, which are the largest s-numbers. This is sharp up to the constant and settles conjectures of Mityagin, Henkin, Carl and Pietsch dating back to 1963. We also extend it to widths of convex sets and discuss optimality there. The proof is elementary.