Maps preserving the bi-skew Jordan product on factor von Neumann algebras

References

[1] Z. Bai and S. Du, The structure of nonlinear Lie derivation on von Neumann algebras, Linear Algebra Appl. 436 (2012), no. 7, 2701–2708. 10.1016/j.laa.2011.11.009Search in Google Scholar

[2] V. Darvish, H. M. Nazari, H. Rohi and A. Taghavi, Maps preserving η-product A ∗ ⁢ B + η ⁢ B ⁢ A ∗ on C ∗ -algebras, J. Korean Math. Soc. 54 (2017), no. 3, 867–876. 10.4134/JKMS.j160286Search in Google Scholar

[3] C. Li, F. Lu and X. Fang, Nonlinear mappings preserving product X ⁢ Y + Y ⁢ X ∗ on factor von Neumann algebras, Linear Algebra Appl. 438 (2013), no. 5, 2339–2345. 10.1016/j.laa.2012.10.015Search in Google Scholar

[4] C. Li, F. Lu and X. Fang, Non-linear ξ-Jordan *-derivations on von Neumann algebras, Linear Multilinear Algebra 62 (2014), no. 4, 466–473. 10.1080/03081087.2013.780603Search in Google Scholar

[5] C. Li, F. Lu and T. Wang, Nonlinear maps preserving the Jordan triple * -product on von Neumann algebras, Ann. Funct. Anal. 7 (2016), no. 3, 496–507. 10.1215/20088752-3624940Search in Google Scholar

[6] C. Li, F. Zhao and Q. Chen, Nonlinear maps preserving product X * ⁢ Y + Y * ⁢ X on von Neumann algebras, Bull. Iranian Math. Soc. 44 (2018), no. 3, 729–738. 10.1007/s41980-018-0048-3Search in Google Scholar

[7] C. J. Li, F. F. Zhao and Q. Y. Chen, Nonlinear skew Lie triple derivations between factors, Acta Math. Sin. (Engl. Ser.) 32 (2016), no. 7, 821–830. 10.1007/s10114-016-5690-1Search in Google Scholar

[8] L. Liu and G.-X. Ji, Maps preserving product X * ⁢ Y + Y ⁢ X * on factor von Neumann algebras, Linear Multilinear Algebra 59 (2011), no. 9, 951–955. 10.1080/03081087.2010.495390Search in Google Scholar

[9] F. Lu and W. Jing, Characterizations of Lie derivations of B ⁢ ( X ) , Linear Algebra Appl. 432 (2010), no. 1, 89–99. 10.1016/j.laa.2009.07.026Search in Google Scholar

[10] W. S. Martindale, III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21 (1969), 695–698. 10.1090/S0002-9939-1969-0240129-7Search in Google Scholar

[11] L. Molnár, A condition for a subspace of ℬ ⁢ ( H ) to be an ideal, Linear Algebra Appl. 235 (1996), 229–234. 10.1016/0024-3795(94)00143-XSearch in Google Scholar

[12] A. Taghavi, V. Darvish and H. Rohi, Additivity of maps preserving products A ⁢ P ± P ⁢ A * on C * -algebras, Math. Slovaca 67 (2017), no. 1, 213–220. 10.1515/ms-2016-0260Search in Google Scholar

[13] A. Taghavi, M. Nouri, M. Razeghi and V. Darvish, A note on non-linear * -Jordan derivations on * -algebras, Math. Slovaca 69 (2019), no. 3, 639–646. 10.1515/ms-2017-0253Search in Google Scholar

[14] A. Taghavi, H. Rohi and V. Darvish, Non-linear *-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), no. 3, 426–439. 10.1080/03081087.2015.1043855Search in Google Scholar