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Linearity of (generalized) \(*\)-Lie derivations and their structures on \(*\)-algebras

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Abstract

Let \( {\mathcal {A}} \) be a unital \(*\)-algebra with characteristic not 2 and containing a nontrivial projection. We show that each nonlinear \(*\)-Lie derivation on \({\mathcal {A}}\) is a linear \(*\)-derivation. Moreover, we characterize nonlinear left \(*\)-Lie centralizers and nonlinear generalized \(*\)-Lie derivations. These results are applied to standard operator algebras and von Neumann algebras in complex Hilbert spaces, which generalize some known results.

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Acknowledgements

The authors are grateful to the anonymous referee for a thorough reading of the manuscript and helpful suggestions. B. Fadaee was supported by the Vice Chancellorship of Research and Technology at the University of Kurdistan under Research Project No. 01/9/11/17885.

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Authors and Affiliations

  1. Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

    Behrooz Fadaee & Hoger Ghahramani

  2. Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC, 28301, USA

    Wu Jing

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  1. Behrooz Fadaee
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  2. Hoger Ghahramani
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  3. Wu Jing
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Correspondence to Behrooz Fadaee.

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Communicated by Shavkat A. Ayupov.

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Fadaee, B., Ghahramani, H. & Jing, W. Linearity of (generalized) \(*\)-Lie derivations and their structures on \(*\)-algebras. Adv. Oper. Theory 9, 20 (2024). https://doi.org/10.1007/s43036-024-00320-1

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  • DOI: https://doi.org/10.1007/s43036-024-00320-1

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