By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections....

In this paper we get some relations between the boundary point spectrum of the generator A of a C0-semigroup and the generator A* of the dual semigroup. This relations combined with the results due to Lyubich-Phong and Arendt-Batty, yield stability results on positive C0-semigroups.

Let $L$, $M$ be Archimedean Riesz spaces and ${ℒ}_b(L,M)$ be the ordered vector space of all order bounded operators from $L$ into $M$. We define a Lamperti Riesz subspace of ${ℒ}_b(L,M)$ to be an ordered vector subspace $ℒ$ of ${ℒ}_b(L,M)$ such that the elements of $ℒ$ preserve disjointness and any pair of operators in $ℒ$ has a supremum in ${ℒ}_b(L,M)$ that belongs to $ℒ$. It turns out that the lattice operations in any Lamperti Riesz subspace $ℒ$ of ${ℒ}_b(L,M)$ are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem for Riesz homomorphisms....