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Research Article | Open Access

Maps on C ∗ -algebras are skew Lie triple derivations or homomorphisms at one point

Zhonghua Wang1, Xiuhai Fei2( )
School of Science, Xi'an Shiyou University, Xi'an, China
School of Mathematics and Physics, West Yunnan University, Lincang, China
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Abstract

In this paper, we show that every continuous linear map between unital C ∗ -algebras is skew Lie triple derivable at the identity is a ∗-derivation and that every continuous linear map between unital C ∗ -algebras which is a skew Lie triple homomorphism at the identity is a Jordan ∗-homomorphism.

Keywords

C∗-algebraskew Lie triple derivationJordan derivationskew Lie triple homomorphism
CLC number: 46L57, 47C15

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 25564-25571
DOI: 10.3934/math.20231305

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Cite this article:
Wang Z, Fei X. Maps on C ∗ -algebras are skew Lie triple derivations or homomorphisms at one point. AIMS Mathematics, 2023, 8(11): 25564-25571. https://doi.org/10.3934/math.20231305

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Received: 18 July 2023
Revised: 15 August 2023
Accepted: 15 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)