In this paper, we show that every continuous linear map between unital $ C^\ast $-algebras is skew Lie triple derivable at the identity is a $ \ast $-derivation and that every continuous linear map between unital $ C^\ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ \ast $-homomorphism.
Citation: Zhonghua Wang, Xiuhai Fei. Maps on $ C^\ast $-algebras are skew Lie triple derivations or homomorphisms at one point[J]. AIMS Mathematics, 2023, 8(11): 25564-25571. doi: 10.3934/math.20231305
In this paper, we show that every continuous linear map between unital $ C^\ast $-algebras is skew Lie triple derivable at the identity is a $ \ast $-derivation and that every continuous linear map between unital $ C^\ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ \ast $-homomorphism.
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Zhonghua Wang, Xiuhai Fei. Maps on $ C^\ast $-algebras are skew Lie triple derivations or homomorphisms at one point[J]. AIMS Mathematics, 2023, 8(11): 25564-25571. doi: 10.3934/math.20231305
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