Nonlinear generalized semi-Jordan triple derivable mappings on completely distributive commutative subspace lattice algebras

Fei Ma; Min Yin; Yanhui Teng; Ganglian Ren; Fei Ma; Min Yin; Yanhui Teng; Ganglian Ren

doi:10.3934/era.2023246

Electronic Research Archive

2023, Volume 31, Issue 8: 4807-4817. doi: 10.3934/era.2023246

Previous Article Next Article

Research article Special Issues

Nonlinear generalized semi-Jordan triple derivable mappings on completely distributive commutative subspace lattice algebras

School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, China

Received: 06 February 2023 Revised: 14 June 2023 Accepted: 28 June 2023 Published: 07 July 2023

In this note we proved that each nonlinear generalized semi-Jordan triple derivable mapping on completely distributive commutative subspace lattice algebras is an additive derivation.
Citation: Fei Ma, Min Yin, Yanhui Teng, Ganglian Ren. Nonlinear generalized semi-Jordan triple derivable mappings on completely distributive commutative subspace lattice algebras[J]. Electronic Research Archive, 2023, 31(8): 4807-4817. doi: 10.3934/era.2023246

Related Papers:

Abstract

In this note we proved that each nonlinear generalized semi-Jordan triple derivable mapping on completely distributive commutative subspace lattice algebras is an additive derivation.

References

[1]	D. Benkovič, Jordan derivations and anti-derivations on triangular matrices, Linear Algebra Appl., 397 (2005), 235–244. https://doi.org/10.1016/j.laa.2004.10.017 doi: 10.1016/j.laa.2004.10.017
[2]	F. Ma, G. Ji, Generalized Jordan derivation on trigular matrix algebra, Linear Multilinear Algebra, 55 (2007), 355–363. https://doi.org/10.1080/03081080601127374 doi: 10.1080/03081080601127374
[3]	H. Ghahramani, Jordan derivations on trivial extensions, Bull. Iranian Math. Soc., 9 (2013), 635–645.
[4]	I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc., 8 (1957), 1104–1110. https://doi.org/10.1090/S0002-9939-1957-0095864-2 doi: 10.1090/S0002-9939-1957-0095864-2
[5]	J. Zhang, W. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl., 419 (2006), 251–255. https://doi.org/10.1016/j.laa.2006.04.015 doi: 10.1016/j.laa.2006.04.015
[6]	C. Li, X. Fang, Lie triple and Jordan derivable mappings on nest algebras, Linear Multilinear Algebra, 61 (2013), 653-666. https://doi.org/10.1080/03081087.2012.703186 doi: 10.1080/03081087.2012.703186
[7]	M. Ashraf, A. Jabeen, Nonlinear Jordan triple higher derivable mappings of triangular algebras, Southeast Asian Bull. Math., 42 (2018), 503–520. https://www.researchgate.net/publication/308966074
[8]	F. Zhao, C. Li, Nonlinear Jordan triple -derivations on von Neumann algebras, Math. Slovaca*, 1 (2018), 163–170. https://doi.org/10.1515/ms-2017-0089 doi: 10.1515/ms-2017-0089
[9]	V. Darvish, M. Nourl, M. Razeghi, A. Taghavi, Nonlinear Jordan triple -derivations on prime -lagebras, Rocky Mountain J. Math., 50 (2020), 543–549. https://doi.org/10.1216/rmj.2020.50.543 doi: 10.1216/rmj.2020.50.543
[10]	G. An, J. He, Characterizations of $(m, n)$-Jordan derivations and $(m, n)$-Jordan derivable mappings on some algebras, Acta Math. Sin., 35 (2019), 378–390. https://doi.org/10.1007/s10114-018-7495-x doi: 10.1007/s10114-018-7495-x
[11]	X. Fei, H. Zhang, A class of nonlinear nonglobal semi-Jordan triple derivable mappings on triangular algebras, J. Math., 2021 (2021). https://doi.org/10.1155/2021/4401874 doi: 10.1155/2021/4401874
[12]	M. Brešar, Jordan mapping of Semiprime Rings, J. Algebra, 127 (1989), 218–228. https://doi.org/10.1016/0021-8693(89)90285-8 doi: 10.1016/0021-8693(89)90285-8
[13]	F. Lu, Jordan triple maps, Linear Algebra Appl., 375 (2003), 311–317. https://doi.org/10.1016/j.laa.2003.06.004 doi: 10.1016/j.laa.2003.06.004
[14]	C. Li, Y. Zhao, F. Zhao, Nonlinear -Jordan-type derivations on -algebras, Rocky Mt. J. Math., 51 (2021), 601–612. https://doi.org/10.1216/rmj.2021.51.601 doi: 10.1216/rmj.2021.51.601
[15]	C. Li, F. Zhao, Q. Chen, Nonlinear skew Lie triple derivations between factors, Acta Math. Sin. (English Series), 32 (2016), 821–830. https://doi.org/10.1007/s10114-016-5690-1 doi: 10.1007/s10114-016-5690-1
[16]	C. Li, F. Lu, Nonlinear maps preserving the Jordan triple -product on von Neumann algebras, Ann. Funct. Anal.*, 7 (2016), 496–507. https://doi.org/10.1007/s11401-018-0086-4 doi: 10.1007/s11401-018-0086-4
[17]	C. Li, F. Lu, Nonlinear maps preserving the Jordan triple 1--product on von Neumann algebras, Complex Anal. Oper. Theory*, 11 (2017), 109–117. https://doi.org/10.1007/s11785-016-0575-y doi: 10.1007/s11785-016-0575-y
[18]	F. Zhao, C. Li, Nonlinear maps preserving the Jordan triple -product between factors, Indagationes Math.*, 29 (2018), 619–627. https://doi.org/10.1016/j.indag.2017.10.010 doi: 10.1016/j.indag.2017.10.010
[19]	W. E. Longstaff, Operators of rank one in reflexive algebras, Can. J. Math., 28 (1976), 9–23. https://doi.org/10.4153/CJM-1976-003-1 doi: 10.4153/CJM-1976-003-1
[20]	M. S. Lambrou, Complete distributivity lattices, Fundamenta Math., 119 (1983), 227–240. https://doi.org/10.4064/FM-119-3-227-240 doi: 10.4064/FM-119-3-227-240
[21]	C. Laurie, W. Longstaff, A note on rank-one operators in reflexive algebras, Proc. Amer. Math. Soc., 89 (1983), 293–297. https://doi.org/10.1090/S0002-9939-1983-0712641-2 doi: 10.1090/S0002-9939-1983-0712641-2
[22]	F. Lu, Derivations of $CDC$ algebras, J. Math. Anal. Appl., 323 (2006), 179–189. https://doi.org/ 10.1016/j.jmaa.2005.10.021 doi: 10.1016/j.jmaa.2005.10.021
[23]	F. Gilfeather, R. L. Moore, Isomorphisms of certain CSL algebras, J. Funct. Anal., 67 (2010), 264–291. https://doi.org/10.1016/0022-1236(86)90039-X doi: 10.1016/0022-1236(86)90039-X
[24]	F. Lu, Lie derivations of certain CSL algebras, Israel J. Math., 155 (2006), 149–156. https://doi.org/10.1007/BF02773953 doi: 10.1007/BF02773953

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)