Polynomially spectrum-preserving maps between commutative Banach algebras

Hatori, Osamu; Miura, Takeshi; Takagi, Hiroyuki

Polynomially spectrum-preserving maps between commutative Banach algebras

Authors

Hatori, Osamu

Miura, Takeshi

Takagi, Hiroyuki

Description

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.
14pages