Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the peripheral point spectrum and the asymptotic behavior of
  irreducible semigroups of Harris operators   Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice
with order continuous norm, we prove that the peripheral point spectrum of its
generator is trivial whenever one of its operators dominates a non-trivial
compact or kernel operator. For a discrete semigroup, i.e. for powers of a
single operator T, we show that the point spectrum of some power T^k intersects
the unit circle at most in 1. As a consequence, we obtain a sufficient
condition for strong convergence of the C_0-semigroup and for a subsequence of
the powers of T, respectively.

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The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ