Abstract
In this chapter, we deal with one-parameter positive semigroups in ordered Banach spaces. Firstly, we discuss the notion of ideally ordered Banach spaces and uniformly order convex Banach spaces. Both classes include Lp-spaces (1 ≤ p < ∞) as well as preduals of von Neumann algebras. We prove several theorems about positive semigroups in such Banach spaces. Then we consider positive semigroups in Banach lattices and investigate several types of asymptotic regularity of these semigroups. In the last section of this chapter, we deal with relations between the geometry of Banach lattices and mean ergodicity of bounded positive semigroups in them.KeywordsBanach SpacePositive OperatorBanach LatticePositive PowerOrder IntervalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
