Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Ordinal Index on the Space of Strictly Singular Operators   Using the notion of $S_\xi$-strictly singular operator introduced by
Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the
subspace of strictly singular operators between two separable Banach spaces. In
our main result, we provide a sufficient condition implying that this index is
bounded by $\omega_1$. In particular, we apply this result to study operators
on totally incomparable spaces, hereditarily indecomposable spaces and spaces
with few operators.

14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci