Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Drazin-meromorphic invertible operators and generalized
  Kato-meromorphic decomposition   A bounded linear operator $T$ on a Banach space $X$ is said to be generalized
Drazin-meromorphic invertible if there exists a bounded linear operator $S$
acting on $X$ such that $TS=ST$, $STS=S$, $ TST-T$ is meromorphic. We shall say
that $T$ admits a generalized Kato-meromorphic decomposition if there exists a
pair of $T$-invariant closed subspaces $(M,N)$ such that $X=M\oplus N$, the
reduction $T_M$ is Kato and the reduction $T_N$ is meromorphic. In this paper
we shall investigate such kind of operators and corresponding spectra, the
generalized Drazin-meromorphic spectrum and the generalized Kato-meromorphic
spectrum, and prove that these spectra are empty if and only if the operator
$T$ is polynomially meromorphic. Also we obtain that the generalized
Kato-meromorphic spectrum differs from the Kato type spectrum on at most
countably many points. Among others, bounded linear operators which can be
expressed as a direct sum of a meromorphic operator and a bounded below (resp.
surjective, upper (lower) semi-Fredholm, Fredholm, upper (lower) semi-Weyl,
Weyl) operator are studied. In particular, we shall characterize the
single-valued extension property at a point $\lambda_0\in\mathbb{C}$ in the
case that $\lambda_0-T$ admits a generalized Kato-meromorphic decomposition. As
a consequence we get several results on cluster points of some distinguished
parts of the spectrum.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an