Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate of decay of s-numbers   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.

3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an