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arXiv · 2208.12611

Nonlinear maps preserving sums of triple products on $\ast $-algebras

João Carlos da Motta Ferreira·Maria das Graças Bruno Marietto
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Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital complex $\ast $-algebras such that $\mathcal{A}$ has a nontrivial projection. In this paper, we study the structure of bijective nonlinear maps $\Phi :\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $\alpha _{1} abc+\alpha _{2} a^{*}cb^{*}+\alpha _{3} ba^{*}c +\alpha _{4} cab^{*}+\alpha _{5} bca+\alpha _{6} cb^{*}a^{*},$ where the scalars $\{\alpha _{k}\}_{k=1}^{6}$ are complex numbers satisfying some conditions.

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João Carlos da Motta Ferreira, Maria das Graças Bruno Marietto. 2022-08-16. Nonlinear maps preserving sums of triple products on $\ast $-algebras. https://arxiv.org/abs/2208.12611

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