Triviality of the peripheral point spectrum

Abstract.

If T _t  = e^Zt is a positive one-parameter contraction semigroup acting on l^p(X) where X is a countable set and 1 ≤ p < ∞, then the peripheral point spectrum P of Z cannot contain any non-zero elements. The same holds for Feller semigroups acting on L^p(X) if X is locally compact.