Commutativity preserving mappings in Banach algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910200970084352 |
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| author | Brešar, M. Escolano, G. M. Peralta, A. Villena, A. R. |
| author_facet | Brešar, M. Escolano, G. M. Peralta, A. Villena, A. R. |
| contents | Let $A$ and $B$ be unital complex Banach algebras having no quotients isomorphic to $\mathbb{C}$ or $M_2(\mathbb{C})$. Assume additionally that $B$ is semisimple. If a surjective additive mapping $Φ\colon A\to B$ satisfies $[Φ(x^2),Φ(x)] = 0$ for all $x\in A$, then there exist a surjective direct sum of an additive homomorphism and an additive anti-homomorphism $Ψ\colon A\to B$, an invertible element $λ\in\mathcal{Z}(B)$, and an additive mapping $ζ\colon A\to\mathcal{Z}(B)$ such that $Φ(x)=λΨ(x)+ζ(x)$ for all $x\in A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commutativity preserving mappings in Banach algebras Brešar, M. Escolano, G. M. Peralta, A. Villena, A. R. Rings and Algebras Functional Analysis Let $A$ and $B$ be unital complex Banach algebras having no quotients isomorphic to $\mathbb{C}$ or $M_2(\mathbb{C})$. Assume additionally that $B$ is semisimple. If a surjective additive mapping $Φ\colon A\to B$ satisfies $[Φ(x^2),Φ(x)] = 0$ for all $x\in A$, then there exist a surjective direct sum of an additive homomorphism and an additive anti-homomorphism $Ψ\colon A\to B$, an invertible element $λ\in\mathcal{Z}(B)$, and an additive mapping $ζ\colon A\to\mathcal{Z}(B)$ such that $Φ(x)=λΨ(x)+ζ(x)$ for all $x\in A$. |
| title | Commutativity preserving mappings in Banach algebras |
| topic | Rings and Algebras Functional Analysis |
| url | https://arxiv.org/abs/2605.07666 |