Additivity of maps preserving triple product on *-ring
DOI:
https://doi.org/10.5269/bspm.40370Abstract
Let A and B be two prime -rings. Let : A ! B be a bijective and satises (A P P) = (A) (P) (P); for all A 2 A and P 2 fI; P1; I ô€€€ P1g where P1 is a projection in A. The operation between two arbitrary elements S and T in A is dened as S T = ST +TS for 2 fô€€€1; 1g. Then, if (I) is projection, we show that is additive.
References
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2. Z. F. Bai, S. P. Du, Multiplicative Lie isomorphism between prime rings, Comm. Algebra 36 (2008) 1626-1633.
3. Z. F. Bai, S. P. Du, Multiplicative -Lie isomorphism between factors, J. Math. Anal. Appl. 346 (2008) 327-335.
4. K. I. Beidar, M. Bresar, M. A. Chebotar, W. S. Martindale, On Herstein’s Lie map conjecture (II), J. Algebra 238 (2001) 239-264.
5. J. Cui, C. K. Li, Maps preserving product XY − Y X on factor von Neumann algebras, Linear Algebra Appl. 431 (2009) 833-842.
6. L. Dai, F. Lu, Nonlinear maps preserving Jordan -products, J. Math. Anal. Appl. 409 (2014) 180-188.
7. H. Gao, -Jordan-triple multiplicative surjective maps on B(H), J. Math. Anal. Appl. 401 (2013) 397–403.
8. P. Ji, Z. Liu, Additivity of Jordan maps on standard Jordan operator algebras, Linear Algebra Appl. 430 (2009) 335-343.
9. C. Li, F. Lu, X. Fang, Nonlinear mappings preserving product XY + Y X on factor von Neumann algebras, Linear Algebra Appl. 438 (2013) 2339-2345.
10. C. Li, F. Lu, Nonlinear maps preserving the Jordan triple 1--product on von Neumann algebras, Complex Analysis and Operator Theory 11 (2017), 109-117.
11. C. Li, F. Lu, T. Wang, Nonlinear maps preserving the Jordan triple -product on von Neumann algebras, Ann. Funct. Anal. 7 (2016), 496-507.
12. F. Lu, Additivity of Jordan maps on standard operator algebras, Linear Algebra Appl. 357 (2002) 123-131.
13. F. Lu, Jordan triple maps, Linear Algebra Appl. 375 (2003) 311-317.
14. W. S. Martindale III, When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21 (1969) 695-698.
15. C. R. Mires, Lie isomorphisms of factors, Trans. Amer. Math. Soc. 147 (1970) 5-63.
16. L. Moln´ar, On isomorphisms of standard operator algebras, Studia Math. 142 (2000) 295-302.
17. A. Taghavi, Maps preserving Jordan triple product on the self-adjoint elements of C-algebras, Asian-European Journal of Mathematics. 10(2) 1750022 (2017) 1-7.
18. A. Taghavi, H. Rohi, V. Darvish, Additivity of maps preserving Jordan -products on C-algebras, Bulletin of the Iranian Mathematical Society. 41 (7) (2015) 107–116
19. A. Taghavi, V. Darvish, H. Rohi, Additivity of maps preserving products AP ± PA on C-algebras, Mathematica Slovaca. 67 (1) (2017) 213–220.
20. V. Darvish, H. M. Nazari, H. Rohi, A. Taghavi, Maps preserving -product AB +BA on C-algebras, Journal of Korean Mathematical Society. 54 (3) (2017) 867–876.
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2020-10-11
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