Regular vector lattices of continuous functions and Korovkin-type theorems-Part II
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....
Regular vector lattices of continuous functions and Korovkin-type theorems-Part I
We introduce and study a new class of locally convex vector lattices of continuous functions on a locally compact Hausdorff space, which we call regular vector lattices. We investigate some general properties of these spaces and of the subspaces of so-called generalized affine functions. Moreover, we present some Korovkin-type theorems for continuous positive linear operators; in particular, we study Korovkin subspaces for finitely defined operators, for the identity operator and for positive...
Representation and duality of multiplication operators on archimedean Riesz spaces
Représentation fonctionnelle des espaces vectoriels toplogiques
Representation of linear operators on spaces of vector valued functions
Representations of topological projector dense lattice algebras
Resolving Banach spaces
R(X) as a Dirichlet Algebra and Representation of Orthogonal Measures by Differentials.