On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators

Details On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators

2012-01-17

arxiv.org/abs/1201.3531v1

Mathematics

Functional Analysis

Scientific paper

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. If the semigroup is discrete, i.e. it consists of 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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