2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227093Let $A$ and $B$ be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials $p$ which satisfy the following property: a map $T$ from $A$ onto $B$ such that the equality \[ σ(p(Tf,Tg))=σ(p(f,g)), \quad f,g \in A \] holds is an algebra isomorphism.14pagesFunctional Analysis46J10, 47B48text