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• # Artykuł - szczegóły

## Open Mathematics

2010 | 8 | 3 | 597-601

EN

### Abstrakty

EN
Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M A and M B, respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M B → M A and a closed and open subset K of M B such that $$\widehat{T\left( a \right)}\left( y \right) = \left\{ \begin{gathered} \widehat{T\left( e \right)}\left( y \right)\hat a\left( {\phi \left( y \right)} \right) y \in K \hfill \\ \widehat{T\left( e \right)}\left( y \right)\overline {\hat a\left( {\phi \left( y \right)} \right)} y \in M_\mathcal{B} \backslash K \hfill \\ \end{gathered} \right.$$ for all a ∈ A, where e is unit element of A. If, in addition, $$\widehat{T\left( e \right)} = 1$$ and $$\widehat{T\left( {ie} \right)} = i$$ on M B, then T is an algebra isomorphism.

EN

597-601

wydano
2010-06-01
online
2010-05-30

### Twórcy

autor
• Niigata University
autor
• Ibaraki University
autor
• Yamagata University

### Bibliografia

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