Rate of decay of s-numbers

2010/09/22 by Timur Oikhberg, Oikhberg, Timur
Mathematics · #46A3 #46B28 #47B10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1009.4278

openalex publication_date 2010/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an operator T ∈ B(X,Y), we denote by a_m(T), c_m(T), d_m(T), and t_m(T) its approximation, Gelfand, Kolmogorov, and absolute numbers. We show that, for any infinite dimensional Banach spaces X and Y, and any sequence α_m \searrow 0, there exists T ∈ B(X,Y) for which the inequality 3 α_{\lceil m/6 \rceil} ≥ a_m(T) ≥ max\c_m(t), d_m(T)\ ≥ min\c_m(t), d_m(T)\ ≥ t_m(T) ≥ α_m/9 holds for every m ∈ \N. Similar results are obtained for other s-scales.

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