Composition operators on Riesz space (Q2772742)

Let \(E\) be an Archimedean Riesz space and \(F\) be a Dedekind complete one. For a positive operator \(S\) from \(E\) to \(F\), consider the set \(H_S\) consisting of composition operators of the form \(\pi\circ S\), where \(\pi\) is any orthomorphism on \(F\). The paper shows that the lattice structure of \(H_S\) is given pointwise. The paper also discusses the algebraic structure of \(H_S\); for example, it is proven that \(H_S\) is an \(f\)-algebra with weak order unit \(S\). The paper concludes with several problems concerning the set \(H_S\).NEWLINENEWLINEFor the entire collection see [Zbl 0972.00067].