Riesz product spaces and representation theory

Abstract

Let {E i:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by ∏ i∈I Ei. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff spaceX such that ∏ i∈I Ei is Riesz isomorphic toC(X) if and only if for everyi∈I there exists a completely regular Hausdorff spaceX i such thatE i is Riesz isomorphic toC(X i).