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arXiv · 1405.4611

Additivity of maps preserving products $AP\pm PA^{*}$ on $C^{*}$-algebras

Ali Taghavi·Vahid Darvish·Hamid Rohi
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Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two prime $C^{*}$-algebras. In this paper, we investigate the additivity of map $Φ$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies $$Φ(AP+λPA^{*})=Φ(A)Φ(P)+λΦ(P)Φ(A)^{*},$$ for all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$ is a nontrivial projection in $\mathcal{A}$ and $λ\in\{-1,+1\}$. Then, $Φ$ is $*$-additive.

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Ali Taghavi, Vahid Darvish, Hamid Rohi. 2015-02-17. Additivity of maps preserving products $AP\pm PA^{*}$ on $C^{*}$-algebras. https://arxiv.org/abs/1405.4611

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