TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Convergence of positive operator semigroups
T2  - Transactions of the American Mathematical Society
N2  - 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.
KW  - Positive semigroups
KW  - semigroup representations
KW  - asymptotic behavior
KW  - kernel operator
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/47859
SN  - 0002-9947
SN  - 1088-6850
VL  - 372
IS  - 9
SP  - 6603
EP  - 6627
PB  - American Mathematical Soc.
CY  - Providence
ER  -