Polynomially spectrum-preserving maps between commutative Banach algebras

Abstract

Let $A$ 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.

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