A Weierstrass-Stone theorem for Choquet simplexes

Subduals and tensor products of spaces of harmonic functions

“…-Since L is a simplex space, the result follows from Proposition 9 of Edwards and Vincent-Smith [13]. Proof.…”

“…[13] will give us that the former subspace is dense in the latter, and, since they are both closed, they will be equal.…”

Uniform approximation of harmonic functions

“…Therefore h < g on ^(X), and by lemma 2, h < g. By Dint's theorem there exists h e L such that f < h < g. Therefore (X, tf, L) is a geometric simplex. We may now extend the density theorem in [13]. Suppose that ^o satisfies condition (a).…”

On the classification of Lindenstrauss spaces

“…If S is a metrizable compact Hausdorff space and TdS is a dense G δ set, is there a compact Choquet simplex with extreme points homeomorphic to T and their closure homeomorphic to SΊ Let Ic C(S) be as above. It is shown in [6] that if X is a Lindenstrauss space, then X is maximal with respect to d x S. That is, if XczY and d γ S = 3 X S, then X = Y. An easy application of Zorn's lemma shows that for any such Ic C(S) there is a maximal Yz) X with respect to d x S. Question 5.…”