Every norm-additive bijection T from C0+(X) to C0+(Y) is given by Tf(y) = h(y) f(τ(y)) for a homeomorphism τ: Y → X and positive continuous h: Y → (0, ∞).
Moln ´ar,Maps on positive cones in operator algebras preserving power means, Aequationes Math.94(2020), 703–722
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Norm additive mappings between the positive cones of continuous function algebras
Every norm-additive bijection T from C0+(X) to C0+(Y) is given by Tf(y) = h(y) f(τ(y)) for a homeomorphism τ: Y → X and positive continuous h: Y → (0, ∞).