Positive Semigroups of Kernel Operators

Extending results of Davies and of Keicher on ℓ^p we show that the peripheral point spectrum of the generator of a positive bounded C₀-semigroup of kernel operators on L^p is reduced to 0. It is shown that this implies convergence to an equilibrium if the semigroup is also irreducible and the fixed space non-trivial. The results are applied to elliptic operators. Dedicated to the memory of H.H. Schaefer