On Norm-Additive Maps Between the Maximal Groups of Positive Continuous Functions


Assume that X and Y are compact Hausdorff spaces. We call C+(X)={f∈C(X):f(x)>0for allx∈X} the maximal positive continuous functions group of C(X). A map T: C+(X) → C+(Y) is called norm-additive, if ‖ Tf+ Tg‖ = ‖ f+ g‖ for all f, g∈ C+(X). We show that any norm-additive map between C+(X) and C+(Y) is a composition operator, and hence the restriction of a norm-additive map between C(X) and C(Y).

Publication Title

Results in Mathematics