Rate of decay of s-numbers

For an operator T ∈ B(X, Y ), we denote by am(T), cm(T), dm(T), and tm(T) its approximation, Gelfand, Kolmogorov, and absolute numbers. We show that, for any infinite dimensional Banach spaces X and Y , and any sequence αm ց 0, there exists T ∈ B(X, Y ) for which the inequality 3α⌈m/6⌉ am(T) max{cm(t), dm(T)} min{cm(t), dm(T)} tm(T) αm/9 holds for every m ∈ N. Similar results are obtained for other s-scales.

• Type: Journal
• Year: 2011
• Where: JAT
• Authors: T. Oikhberg
• Keywords: Absolute Numbers, Infinite Dimensional Banach, JAT 2011, Sequence αm