@article{GerlachGlueck2019,
  author    = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen},
  title     = {Convergence of positive operator semigroups},
  series = {Transactions of the American Mathematical Society},
  volume    = {372},
  journal   = {Transactions of the American Mathematical Society},
  number    = {9},
  publisher = {American Mathematical Soc.},
  address   = {Providence},
  issn      = {0002-9947},
  doi       = {10.1090/tran/7836},
  pages     = {6603 -- 6627},
  year      = {2019},
  abstract  = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.},
  language  = {en}
}