It is proved that a linear surjection $\Phi 𝒜\to ℬ$, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.

Let A and B be uniform algebras. Suppose that α ≠ 0 and A 1 ⊂ A. Let ρ, τ: A 1 → A and S, T: A 1 → B be mappings. Suppose that ρ(A 1), τ(A 1) and S(A 1), T(A 1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A 1, S(e 1)−1 ∈ S(A 1) and S(e 1) ∈ T(A 1) for some e 1 ∈ A 1 with ρ(e 1) = 1, then there exists a real-algebra isomorphism $$\tilde{S}$$ : A → B such that $$\tilde{S}$$ (ρ(f)) = S(e 1)−1 S(f) for every f ∈ A 1. We also give some applications...