von Neumann代数中CSL子代数上的Jordan (α,β)-导子
Jordan (α,β)-Derivations on CSL Subalgebras of von Neumann Algebras
设A是Hilbert空间H上的von Neumann代数的CSL子代数.本文证明了,在一定的条件下,A上的Jordan (α,β)-导子是(α,β)-导子,其中α,β是A上的两个自同构.还证明了在没有添加任何条件的情况之下,CSL代数上的任意Jordan (α,β)-导子是(α,β)-导子.另外,讨论了von Neumann代数中的CSL子代数上的n次幂(α,β)-映射.
Let A be a CSL subalgebra of a von Neumann algebra on a Hilbert space H.It is shown that a Jordan (α,β)-derivation on A is an (α,β)-derivation under a mild condition,where α,β are automorphisms on A.It is also shown that any Jordan (α,β)-derivation on a CSL algebra is an (α,β)-derivation with no additional conditions being assumed.We also investigate the n-th power (α,β)-maps on CSL subalgebras of von Neumann algebras.
Jordan &sigma / -导子 / Jordan (&alpha / &beta / )-导子 / von Neumann代数的CSL子代数 {{custom_keyword}} /
Jordan σ-derivations / Jordan (α,β)-derivations / CSL subalgebras of von Neumann algebras {{custom_keyword}} /
[1] Ashraf M., Ali A., Ali S., On Lie ideals and generalized (φ, θ)-derivations in prime rings, Comm. Algebra, 2004, 32:2977-2985.
[2] Benkovi? D., Jordan σ-derivations of triangular algebras, Linear Multilinear Algebra, 2016, 64:143-155.
[3] Brešar M., Vukman M., Jordan (θ, φ)-derivations, Glasnik Math., 1991, 26:13-17.
[4] Brešar M., Jordan derivations revisited, Math. Pro. Camb. Phil. Soc., 2005, 139:411-425.
[5] Brešar M., Jordan derivations on semiprime rings, Proc. Amer. Math. Soc., 1988, 104:1003-1006.
[6] Gilfeather F., Moore R. L., Isomorphisms of certain CSL algebras, J. Funct. Anal., 1986, 67:264-291.
[7] Han D., Wei F., Jordan (α, β)-derivations on triangular algebras and related mappings, Linear Algebra Appl., 2011, 434:259-284.
[8] Herstein J. M., Topics in Ring Theory, University of Chicago Press, Chicago, 1969.
[9] Hou C., Meng Q., Continuity of (α, β)-derivations of operator algebras, J. Korean Math. Soc., 2011, 48:823-835.
[10] Jiao M., Hou J., Additive maps derivable or Jordan derivable at zero point on nest algebras, Linear algebra Appl., 2010, 432:2984-2994.
[11] Lanski C., Generalized derivations and nth power maps in rings, Comm. Algebra, 2007, 35:3660-3672.
[12] Lee T., Functional identities and Jordan σ-derivations, Linear Multilinear Algebra, 2016, 64:221-234.
[13] Li P., Han D., Tang W., Centralizers and Jordan derivations for CSL subalgebras of von Neumann algebras, J. Oper. Theory. 2013, 69:117-133.
[14] Lu F., The Jordan structure of CSL algebras, Studia Math., 2009, 190(3):283-299.
[15] Qi X., Hou J., Generalized skew derivations on nest algebras charaterized by acting on zero products, Publ. Math. Debrecen, 2011, 78:457-468.
国家自然科学基金(11401273,11371279);江西省教育厅科学技术研究项目(GJJ160915);江西省普通本科高校中青年教师发展计划访问学者专项资金;江西省远航工程资助项目
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