Polynomially spectrum-preserving maps between commutative Banach algebras

Osamu Hatori; Takeshi Miura; Hiroyuki Takagi

Polynomially spectrum-preserving maps between commutative Banach algebras

Functional Analysis 2009-04-16 v1

Authors: Osamu Hatori , Takeshi Miura , Hiroyuki Takagi

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

Keywords

banach algebras graph polynomials mapping theory

Cite

@article{arxiv.0904.2322,
  title  = {Polynomially spectrum-preserving maps between commutative Banach algebras},
  author = {Osamu Hatori and Takeshi Miura and Hiroyuki Takagi},
  journal= {arXiv preprint arXiv:0904.2322},
  year   = {2009}
}

Comments

14pages

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