The maximal difference theorem for s-numbers
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…
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