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.
Positivity – Springer Journals
Published: Nov 2, 2012
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