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Abstract
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Let $ \mathcal{A} $ be a unital $ \star $-algebra and $ \varphi : \mathcal{A} \to \mathcal{A} $ be a linear map. We consider $ \varphi $ behaving like (right, left) centralizer at the following orthogonality conditions on elements of $ \mathcal{A} $: $ a b^\star = 1 $ and $ a^\star b = 1 $ and we characterize such maps. Indeed we prove that $ \varphi $ is a $ \star $-(right, left) centralizer if, and only if, $ \delta $ is a $ \star $-(right, left) centralizer at $ 1 $.
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