2018/02/14 by Jochen Glück, Glück, Jochen, Manfred Wolff +1
Mathematics · #46B40 #47A35 #47B60 #47C15 #47D06 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1802.05364
openalex publication_date 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider positive operator semigroups on ordered Banach spac -es and study\nthe relation of their long time behaviour to two different domination\nproperties. First, we analyse under which conditions almost periodicity and\nmean ergodicity of a semigroup \T are inherited by other semigroups\nwhich are asymptotically dominated by \T. Then, we consider\nsemigroups whose orbits asymptotically dominate a positive vector and show that\nthis assumption is often sufficient to conclude strong convergence of the\nsemigroup as time tends to infinity.\n Our theorems are applicable to time-discrete as well as time-continuous\nsemigroups. They generalise several results from the literature to considerably\nlarger classes of ordered Banach spaces.\n