{"id":"palomar/PALOMAR-2026-09-07-000008","url":"https://github.com/mario-ullrich/Lean-SNumbers/tree/085b29905f46bc4e61e19be642699153bdb99c2d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-07-000008-v1.json","repo":"https://github.com/mario-ullrich/Lean-SNumbers","tags":["math.FA","math.OA","msc:47B06","msc:47L20","msc:46B06","msc:41A46","functional-analysis","s-numbers","operator-theory"],"score":0,"title":"The maximal difference theorem for s-numbers","trust":"high","domain":"math.FA","source":"palomar","authors":["Mario Ullrich"],"reviews":0,"subject":"math.FA","summary":"A bound between all s-numbers (in the sense of Pietsch). The approximation numbers a_n are the largest s-number sequence and the Hilbert numbers h_n the smallest, so that h_n(S) <= s_n(S) <= a_n(S) holds for every s-number sequence (s_n) and every bounded linear operator S between Banach spaces. The formalized result gives a bound in the reverse direction: a_n(S) <= ((n+1)^(n+1)/n^n) * h_n(S) <= e * (n+1) * h_n(S), for every bounded linear operator between normed spaces over the reals or the complex numbers. Hence, the same factor bounds the gap between any two s-number sequences. The linear…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-07","reactions":{},"formalized":true,"formalizes":[{"title":"On bounds between all s-numbers and widths of convex sets","identifier":"arXiv:2608.05024","relationship":"formalizes"}]}