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arXiv · 2108.00025

$*$-Lie-type maps on $C^*$-algebras

Ruth Nascimento Ferreira·Bruno Leonardo Macedo Ferreira·Henrique Guzzo Junior·Bruno Tadeu Costa
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Abstract

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial symmetric projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $*$-Lie-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative $*$-Lie-type map is $*$-isomorphism.

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Ruth Nascimento Ferreira, Bruno Leonardo Macedo Ferreira, Henrique Guzzo Junior, Bruno Tadeu Costa. 2021-07-30. $*$-Lie-type maps on $C^*$-algebras. https://arxiv.org/abs/2108.00025

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