Norm-additive in modulus maps between function algebras

The main purpose of this paper is to characterize norm-additive in modulus, not necessarily linear, maps defined between function algebras (not necessarily unital or uniformly closed). In fact, for function algebras A and B on locally compact Hausdorff spaces X and Y , respectively, we study surjections T,S : A −→ B satisfying ∥|Tf| + |Sg|∥Y = ∥|f| + |g|∥X for all f, g ∈ A