Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on variation of spectral subspaces under J-self-adjoint
  perturbations   Let $A$ be a self-adjoint operator on a Hilbert space $\fH$. Assume that the
spectrum of $A$ consists of two disjoint components $\sigma_0$ and $\sigma_1$.
Let $V$ be a bounded operator on $\fH$, off-diagonal and $J$-self-adjoint with
respect to the orthogonal decomposition $\fH=\fH_0\oplus\fH_1$ where $\fH_0$
and $\fH_1$ are the spectral subspaces of $A$ associated with the spectral sets
$\sigma_0$ and $\sigma_1$, respectively. We find (optimal) conditions on $V$
guaranteeing that the perturbed operator $L=A+V$ is similar to a self-adjoint
operator. Moreover, we prove a number of (sharp) norm bounds on variation of
the spectral subspaces of $A$ under the perturbation $V$. Some of the results
obtained are reformulated in terms of the Krein space theory. As an example,
the quantum harmonic oscillator under a PT-symmetric perturbation is discussed.

19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ