Abstract
Let \(\mathcal {N}\) be a non-trivial nest on a Hilbert space H and \(\textrm{alg}\mathcal {N}\) be the associated nest algebra. Let \(G\in \textrm{alg}\mathcal {N}\) be an operator with \(\overline{\textrm{ran}(G)}\in \mathcal {N}\backslash \{H\}\). In this note, we give a description of Lie derivable maps and generalized Lie 2-derivable maps at G of nest algebra \(\textrm{alg}\mathcal {N}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
References
An, R., Cai, Y.: Derivations and derivable maps on von Neumann algebras. Linear Multilinear Algebra 69, 2806–2812 (2021)
Davision, K.R.: Nest Algebras Harlow: Longmans; (Pitman research notes in mathematics series; 191) (1988)
Du, Y., Wang, Y.: Lie derivations of generalized matrix algebras. Linear Algebra Appl. 437, 2719–2726 (2012)
Hou, J., An, R.: Additive maps on rings behaving like derivations at idempotent-product elements. J. Pure Appl. Algebra 215, 1852–1862 (2011)
Ji, P., Qi, W.: Characterizations of Lie derivations of triangular algebras. Linear Algebra Appl. 435, 1137–1146 (2011)
Liu, L., Gao, K.: Characterizations of Lie centralizers of triangular algebras. Linear Multilinear Algebra 71, 2375–2391 (2023)
Liu, L., Li, K.: On Lie derivations of triangular algebras Rocky Mountain J. Math. in press
Lu, F., Jing, W.: Characterizations of Lie derivations of \(B(X)\). Linear Algebra Appl. 432, 89–99 (2010)
Pan, Z.: Derivable maps and generalized derivations on nest and standard algebras Demonstr. Math. 49, 331–344 (2016)
Qi, X., Hou, J.: Characterizations of derivations of Banach space nest algebras: All-derivable points. Linear Algebra Appl. 432, 3183–3200 (2010)
Zhu, J., Zhao, S.: Characterizations of all-derivable points in nest algebras Proc. Am. Math. Soc. 141, 2343–2350 (2013)
Acknowledgements
The authors wish to give their thanks to the referees and the editor for their helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Additional information
Communicated by Kunyu Guo.
This work was completed with the support of the National Natural Science Foundation of China (No. 12071134)
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, L., Li, K. Lie derivable maps on nest algebras. Ann. Funct. Anal. 15, 14 (2024). https://doi.org/10.1007/s43034-023-00315-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s43034-023-00315-8