On the kernel of a Markov projection on 𝐶(𝑋)

Abstract

Let X X be a compact metric space and L L a closed linear subspace of C ( X ) C(X) , the real valued continuous functions on X X . We give necessary and sufficient conditions of an algebraic nature for L L to be the kernel of a Markov projection P P on C ( X ) C(X) . We also characterize compact spaces for which our result holds as those for which the Borsuk-Dugundji simultaneous extension theorem holds.