Affine projections on adapted subalgebras of continuous functions

In this paper we study a particular class of positive projections defined on an adapted subalgebra of continuous real-valued functions. Among other things, we characterize the existence of such projections in terms of representing measures concentrated on the Choquet boundary and we show their strong connection with the abstract Dirichlet problem. Finally we show how to construct Korovkin subsets for such projections.