We consider one-parameter semigroups of linear operators etA on C(K) such that for every f>0 there exists t0>0 so that etAf>0 for all t>t0. The purpose of the talk is to give a general theory of such eventually positive semigroups and characterise them in terms of positivity properties of the resolvent (λI-A)-1 and the spectral projection associated with the spectral bound.
Examples of eventually positive semigroups include the semigroup generated by the Dirichlet-to-Neumann operator, delay differential equations, higher order parabolic equations and some matrix semigroups.
This is joint work with Wolfgang Arendt, Jochen Glück and James Kennedy.