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

Research paper by Moritz Gerlach

Indexed on: 06 Nov '12Published on: 06 Nov '12Published in: Mathematics - Functional Analysis

#### Abstract

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.