Polynomially spectrum-preserving maps between commutative Banach algebras

Details Polynomially spectrum-preserving maps between commutative Banach algebras Polynomially spectrum-preserving maps between commutative Banach algebras

2009-04-15

arxiv.org/abs/0904.2322v1

Mathematics

Functional Analysis

14pages

Scientific paper

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 \[ \sigma
(p(Tf,Tg))=\sigma (p(f,g)), \quad f,g \in A \] holds is an algebra isomorphism.

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