On Norm-Additive Maps Between the Maximal Groups of Positive Continuous Functions
Abstract
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
Recommended Citation
Chen, L., Dong, Y., & Zheng, B. (2019). On Norm-Additive Maps Between the Maximal Groups of Positive Continuous Functions. Results in Mathematics, 74 (4) https://doi.org/10.1007/s00025-019-1076-x
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