Non-linear New Product ½ (AB*C+CB*A) Derivations on *-Algebras
DOI:
https://doi.org/10.5269/bspm.65221Resumen
Let A be a prime -algebra with unit I and a nontrivial projection.
Then the map : A ! A satises in the following condition
(fABCg) = f(A)BCg + fA(B)Cg + fAB(C)g
where fABCg = 1
2 (ABC + CBA) for all A;B;C 2 A, is additive.
Moreover, if (I) is self-adjoint, then is a -derivation.
Referencias
1. Christensen, E., Derivitions of nest algebras, Ann. Math. 229, 155-161 (1977)
2. Dai, L., Lu, F., Nonlinear maps preserving *-Jordan products, J. Math. Anal. Appl. 409, 180-188 (2014)
3. Darvish, V., Nouri, M., Razeghi, M., Taghavi, A. Maps preserving Jordan and *-Jordan triple product on operator *-algebras, Bulletin of the koream Mathematical Society. 56, 451-459 (2019)
4. Darvish, V., Rohi, H., Taghavi, A., Nanlinear *-Jordan derivation on von Neumann algebras, Linear and Multilinear Algebra. 64, 426-439 (2016)
5. Darvish, V., Rohi, H., Taghavi, A., Additivity of maps preserving products AP +- PA* on C*-algebras, Mathematica Slovaca. 67, 213-220 (2017)
6. Fang, X., Li, C., Lu, F., Nonlinear mappings preserving products XY +- Y X* on factor van Neumann algebras, Linear Algebra Appl. 438, 2339-2345 (2013)
7. Herstein, I. N., Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8, 1104-1110 (1957)
8. Ma, D., Pang, Y., Zhang, D., The second nonlinear mixed Jordan triple derivable mapping on factor van Neumann algebras, Bulletin of the Iranian Mathematical Society. 48, 951-962 (2022)
9. Sakai, S., Derivations of W*-algebras, Ann. Math. 83, 273-279 (1966)
10. Semrl, P., Additive derivations of some operator algebras, Illinois J. Math. 35, 234-240 (1991)
11. Semrl, P., Ring derivations on standard operator algebras, J. Funct. Anal. 112, 318-324 (1993)
12. Semrl, P., Jordan *-derivations of standard operator algebras, Proc. Amer. Math. Soc. 120, 515-519 (1994)
13. Taghavi, A., Tavakoli, E., Additivity of maps preserving Jordan triple products on prime C*-algebras, Annals of Functional Analysis. Springer. 11, 391-405 (2020)
2. Dai, L., Lu, F., Nonlinear maps preserving *-Jordan products, J. Math. Anal. Appl. 409, 180-188 (2014)
3. Darvish, V., Nouri, M., Razeghi, M., Taghavi, A. Maps preserving Jordan and *-Jordan triple product on operator *-algebras, Bulletin of the koream Mathematical Society. 56, 451-459 (2019)
4. Darvish, V., Rohi, H., Taghavi, A., Nanlinear *-Jordan derivation on von Neumann algebras, Linear and Multilinear Algebra. 64, 426-439 (2016)
5. Darvish, V., Rohi, H., Taghavi, A., Additivity of maps preserving products AP +- PA* on C*-algebras, Mathematica Slovaca. 67, 213-220 (2017)
6. Fang, X., Li, C., Lu, F., Nonlinear mappings preserving products XY +- Y X* on factor van Neumann algebras, Linear Algebra Appl. 438, 2339-2345 (2013)
7. Herstein, I. N., Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8, 1104-1110 (1957)
8. Ma, D., Pang, Y., Zhang, D., The second nonlinear mixed Jordan triple derivable mapping on factor van Neumann algebras, Bulletin of the Iranian Mathematical Society. 48, 951-962 (2022)
9. Sakai, S., Derivations of W*-algebras, Ann. Math. 83, 273-279 (1966)
10. Semrl, P., Additive derivations of some operator algebras, Illinois J. Math. 35, 234-240 (1991)
11. Semrl, P., Ring derivations on standard operator algebras, J. Funct. Anal. 112, 318-324 (1993)
12. Semrl, P., Jordan *-derivations of standard operator algebras, Proc. Amer. Math. Soc. 120, 515-519 (1994)
13. Taghavi, A., Tavakoli, E., Additivity of maps preserving Jordan triple products on prime C*-algebras, Annals of Functional Analysis. Springer. 11, 391-405 (2020)
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Publicado
2025-03-24
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Research Articles
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Cómo citar
Kazemi, F., & Taghavi, A. (2025). Non-linear New Product ½ (AB*C+CB*A) Derivations on *-Algebras. Boletim Da Sociedade Paranaense De Matemática, 43, 1-5. https://doi.org/10.5269/bspm.65221
