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arXiv · 2211.01326

Mappings preserving sum 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 mappings $Φ:\mathcal{A}\rightarrow \mathcal{B}$ preserving sum of triple products $α_{1} ab^{*}c+α_{2} acb^{*}+α_{3} b^{*}ac +α_{4} cab^{*}+α_{5} b^{*}ca+α_{6} cb^{*}a,$ where the scalars $\{α_{k}\}_{k=1}^{6}$ are complex numbers satisfying some conditions. Applications of obtained results are given.

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João Carlos da Motta Ferreira, Maria das Graças Bruno Marietto. 2022-09-14. Mappings preserving sum of triple products on $\ast $-algebras. https://arxiv.org/abs/2211.01326

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