Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of rank one perturbations of normal operators with lacunary
  spectrum   Suppose $\mathcal{A}$ is a compact normal operator on a Hilbert space $H$
with certain lacunarity condition on the spectrum (which means, in particular,
that its eigenvalues go to zero exponentially fast), and let $\mathcal{L}$ be
its rank one perturbation. We show that either infinitely many moment
equalities hold or the linear span of root vectors of $\mathcal{L}$,
corresponding to non-zero eigenvalues, is of finite codimension in $H$. In
contrast to classical results, we do not assume that the perturbation is weak.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs