Abstract
In this paper, we characterize the *-Jordan semi-triple derivable mappings (i.e. a mapping Φ from * algebra \(\mathcal{A}\) into \(\mathcal{A}\) satisfying Φ(AB*A) = Φ(A)B*A + AΦ(B)*A + AB* Φ(A) for every A, B \(\mathcal{A}\)) in the finite dimensional case and infinite dimensional case.
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References
M. Brešar, Jordan mappings of semiprime rings, J. Algebra, 127 (1989), 218–228.
W. Du and J. Zhang, Jordan semi-triple derivable maps of matrix algebras, Acta Math. Sinica, 51 (2008), 571–578.
H. Gao, *-Jordan-triple multiplicative surjective maps on \(\mathcal{B}(\mathcal{H})\), J. Math. Anal. Appl., 401 (2013), 397–403.
G. Lešnjak and N. S. Sze, On injective Jordan semi-triple maps of matrix algebras, Linear Algebra Appl., 414 (2006), 383–388.
J. Hakeda, Additivity of *-semigroup isomorphisms among *-algebra, Bull. Lond. Math. Soc., 18 (1986), 51–56.
I. N. Herstein, Jordan Derivations of prime rings, Proc. Amer. Math. Soc., 8 (1957), 1104–1110.
W. Jing and F. Lu, Lie derivable mappings on prime rings, Comm. Algebra, 40 (2012), 2700–2719.
W. Jing, Nonlinear *-Lie derivation of standard operator algebras, Questions. Math., 39 (2016), 1037–1046.
R. V Kadison, Derivations of operator algebras, Ann. Math., 83 (1966), 280–293.
C. Li, F. Lu, and X. Fang, Nonlinear ξ-Jordan *-derivations on von Neumann algebras, Linear Multilinear Algebra, 62 (2014), 466–473.
C. Li and X. Fang, Lie triple and Jordan derivable mappings on nest algebras, Linear Multilinear Algebra, 61 (2013), 653–666.
F. Lu and B. Liu, Lie derivable maps on B(X), J. Math. Anal. Appl., 372 (2010), 369–376.
F. Lu, Additivity of Jordan maps on standard operator algebras, Linear Algebra Appl., 357 (2002), 123–131.
F. Lu, Jordan triple maps, Linear Algebra Appl., 375 (2003), 311–317.
F. Lu, Jordan derivable maps of prime rings, Commun. Algebra, 38 (2010), 4430–4440.
W. S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc., 21 (1969), 695–698.
L. Molnár, On isomorphisms of standard operator algebras, Stud. Math., 142 (2000), 295–302.
L. Molnár, Jordan maps on standard operator algebras, in: Functional Equations Result sand Advances, Kluwer Academic Publishers, Dordrecht 2002.
S. Sakai, Derivations of W*-algebras, Ann. Math., 83 (1966), 273–279.
P. Šemrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc., 123 (1995), 1851–1855.
W. Yu and J. Zhang, Nonlinear *-Lie derivations on factor von Neumann algebras, Linear Algebra Appl., 437 (2012), 1979–1991.
Acknowledgement
The authors wish to thank anonymous reviewers for their constructive and valuable suggestions which have considerably improved the presentation of the paper. This work was supported by the National Natural Science Foundation of China (No. 11471199, No. 11601010) and the Postdoctoral Science Foundation of China (No. 2018M633450). The first author is supported by Foundation of Educational Commission (No. KY[2017]092) and of Science and Technology Department (No. [2018]1001) of Guizhou Province of China.
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Chen, L., Zhang, J. *-Jordan Semi-Triple Derivable Mappings. Indian J Pure Appl Math 51, 825–837 (2020). https://doi.org/10.1007/s13226-020-0434-4
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DOI: https://doi.org/10.1007/s13226-020-0434-4