We consider convex monotone semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a σ -Dedekind complete Banach lattice with an additional assumption on the dual space. As typical examples, we consider the space of bounded uniformly continuous functions and the space of...

In this paper, we investigate convex semigroups on Banach lattices. First, we consider the case, where the Banach lattice is σ-Dedekind complete and satisfies a monotone convergence property, having Lp-spaces in mind as a typical application. Second, we consider monotone convex semigroups on a...