This is an announcement for the paper "Rate of decay of s-numbers" by Timur Oikhberg.

Abstract: For an operator $T \in B(X,Y)$, 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 $\alpha_m \searrow 0$, there exists $T \in B(X,Y)$ for which the inequality $$ 3 \alpha_{\lceil m/6 \rceil} \geq a_m(T) \geq \max{c_m(t), d_m(T)} \geq \min{c_m(t), d_m(T)} \geq t_m(T) \geq \alpha_m/9 $$ holds for every $m \in \N$. Similar results are obtained for other $s$-scales.

Archive classification: math.FA math.NA

Mathematics Subject Classification: 46A3, 46B28, 47B10

Submitted from: toikhber@math.uci.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1009.4278

or

http://arXiv.org/abs/1009.4278