Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation analysis of $A_{T,S}^{(2)}$ on Hilbert spaces   In this paper, we investigate the perturbation analysis of $A_{T,S}^{(2)}$
when $T,\,S$ and $A$ have some small perturbations on Hilbert spaces. We
present the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable.
The explicit representation for the perturbation of $A_{T,S}^{(2)}$ and the
perturbation bounds are also obtained.

6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org