References

A CHARACTERIZATION OF ADDITIVE DERIVATIONS ON VON NEUMANN ALGEBRAS


[1] M. Brešar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.

[2] M. Brešar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. R. Soc. Edinb., Sect. A 137 (2007), 9-21.

[3] J. A. Brooke, P. Busch and B. Pearson, Commutativity up to a factor of bounded operators in complex Hilbert spaces, R. Soc. Lond. Proc. Ser. A Math Phys. Eng. Sci. A 458 (2002), 109-118.

[4] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.

[5] J. C. Hou and X. F. Qi, Additive maps derivable at some points on lattice algebras, Lin. Alg. Appl. 429 (2008), 1851-1863.

[6] B. E. Johnson, Symmetric amenability and the non-existence of Lie and Jordan derivations, Math. Proc. Cambridge Philos. Soc. 120 (1996), 455-473.

[7] P. S. Ji and W. Q. Qi, Characterizations of Lie derivations of triangular algebras, Linear Algebra and its Applications 435(5) (2011), 1137-1146.

[8] C. Kassel, Quantum Groups, Springer-Verlag, New York, 1995.

[9] L. Liu and G. X. Ji, derivable maps and generalized derivable maps on standard operator algebras, Preprint.

[10] F. Lu and W. Ji, Characterizations of Lie derivations of Lin. Alg. Appl. 432 (2009), 89-99.

[11] M. Mathieu and A. R. Villena, The structure of Lie derivations on J. Funct. Anal. 202 (2003), 504-525.

[12] C. R. Miers, Lie isomorphisms of operator algebras, Pacific J. Math. 38 (1971), 717-735.

[13] X. F. Qi and J. C. Hou, Additive Lie derivations and generalized Lie derivations on Nest algebras, Lin. Alg. Appl. 431 (2009), 843-854.

[14] X. F. Qi and J. C. Hou, Linear maps Lie derivable at zero on lattice algebras, Studia Math. 197 (2010), 157-169.

[15] X. F. Qi and J. C. Hou, Characterization of Lie derivations on prime rings, Communication in Algebras 39(10) (2011), 3824-3835.

[16] X. F. Qi, J. Cui and J. C. Hou, Characterizing additive derivations of prime algebras by zero products, Lin. Alg. Appl. 434 (2011), 669-682.

[17] X. F. Qi and J. C. Hou, Additive Lie derivations and generalized Lie derivations on prime algebras, Acta Math. Sin., English Series 29(2) (2013), 383-392.

[18] W. L. Yang and J. Zhu, Characterizations of additive (generalized) derivations on triangular algebras, Linear and Multilinear Algebras 61(6) (2013), 811-830.