因子von Neumann代数上的非线性混合ξ-Jordan三重可导映射
Nonlinear Mixed ξ-Jordan Triple Derivable Maps on Factor von Neumann Algebras
设A是一个的因子von Neumann代数.我们证明了每一个非线性混合ξ-Jordan(ξ≠0,-1)三重可导映射φ:A → A都是可加的*-导子,且对任意的A ∈ A,有φ(ξA)=ξφ(A).
Let A be a factor von Neumann algebra. We prove that each nonlinear mixed ξ-Jordan triple derivable map φ:A → A is an additive *-derivation and φ(ξA)=ξφ(A) for all A ∈ A with ξ≠ 0, -1
因子von Neumann代数 / 混合&xi / -Jordan三重可导映射 / *-导子 {{custom_keyword}} /
factor von Neumann algebra / mixed ξ-Jordan triple derivable map / *-derivation {{custom_keyword}} /
[1] Ashraf M., Jabeen A., Nonlinear Jordan triple derivable mappings on triangular algebras, Pac. J. Appl. Math., 2015, 7:225-235.
[2] Dai L., Lu F., Nonliear maps preserving Jordan *-product, J. Math. Anal. Appl., 2014, 409:180-188.
[3] Han D., Additive derivations of nest algebras, Proc. Amer. Math. Soc., 1993, 119:1165-1169.
[4] Huo D., Zheng B., Liu H., Nonlinear maps preserving Jordan triple η-*-products, J. Math. Anal. Appl., 2015, 430:830-844.
[5] Li C., Lu F., Fang X., Nonlinear ξ-Jordan *-derivations on von Neumann algebras, Linear and Multilinear Algebra, 2014, 62:466-473.
[6] Li C., Lu F., Fang X., Nonlinear mappings preserving product XY + YX* on factor von Neumann algebras, Linear Algebral., 2013, 438:2339-2345.
[7] Lu F., Jordan derivable maps of prime rings, Comm. Algebra, 2010, 38:4430-4440.
[8] Šemrl P., On Jordan *-derivations and an application, Colloq. Math., 1990, 59:241-251.
[9] Šemrl P., Jordan *-derivations of standard operator algebras, Proc. Amer. Math. Soc., 1994, 120:515-519.
[10] Taghavi A., Rohi H., Darvish V., Nonlinear *-Jordan derivations on von Neumann algebras, Linear and Multilinear Algebra, 2016, 64:426-439.
[11] Zhang F., Nonlinear skew Jordan derivable maps on factor von Neumann algebras, Linear and Multilinear Algebra, 2016, 64:2090-2103.
[12] Zhang J., Yu W., Jordan derivations of triangular algebras, Linear Algebra Appl., 2006, 419:251-255.
[13] Zhao F., Li C., Nonlinear maps preserving the Jordan triple *-product between factors, Indagationes Mathematicae, 2018, 29:619-627.
国家自然科学基金资助项目(11471199)
/
〈 | 〉 |