In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it...

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...

In this paper we construct the smallest semigroup S that dominates a given family of linear Feller semigroups. The semigroup S will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong continuity properties of the semigroup envelope and show that it...

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...