Eventually Positive Semigroups of Linear Operators

Daniel Daners, Jochen Glück, and James B Kennedy
Preprint, February 2015
Journal of Mathematical Analysis and Applications 433 (2016), 1561–1593.
Original available at DOI 10.1016/j.jmaa.2015.08.050
Citations on Google Scholar


We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy problem is positive for large enough time. Characterisations of such semigroups are given by means of resolvent properties of the generator and Perron-Frobenius type spectral conditions.

We apply these characterisations to prove eventual positivity of several examples of semigroups including some fourth order elliptic equations and classes of delay-differential equations. Other examples show that the theory is optimal. We also consider eventually positive semigroups on arbitrary Banach lattices and establish several results for their spectral bound which were previously only known for positive semigroups.

You can go to the original article or download a preprint version arXiv:1511.05294 [math.FA].