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Articles

Multiplicative ∗-Jordan type higher derivations on von Neumann algebras

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Pages 1689-1711 | Received 28 Mar 2019, Published online: 26 Sep 2019

References

  • R.-L. An and J.-C. Hou, A characterization of ∗-automorphism on B(H), Acta. Math. Sinica (English Series) 26 (2010), 287–294.
  • M. Ashraf and N. Parveen, On Jordan triple higher derivable mappings in rings, Mediterr. J. Math. 13(4) (2016), 1465–1477.
  • M. Ashraf and N. Parveen, Lie triple higher derivable maps on rings, Communications in Algebra 45(5) (2017), 2256–2275.
  • M. Ashraf and B.A. Wani, Multiplicative ∗- Lie triple higher derivations on von Neumann algebras, Math. Reports, to appear.
  • M. Ashraf, B.A. Wani, and F. Wei, Multiplicative ∗- Lie triple higher derivations on standard operator algebras, Quaest. Math. https://doi.org/10.2989/16073606.2018.1502213.
  • M. Ashraf, B.A. Wani, and F. Wei, Multiplicative ∗- Lie type higher derivations of standard operator algebras, preprint
  • M. Ashraf, B.A. Wani, and F. Wei, Multiplicative ∗- Lie type higher derivations on von Neumann algebras, preprint
  • Z.-F. Bai and S.-P. Du, The structure of nonlinear Lie derivation on von Neumann algebras, Linear Algrbra Appl. 436 (2012), 2701–2708.
  • Z.-F. Bai and S.-P. Du, Maps preserving products XY −Y X∗ on von Neumann algebras, J. Math. Anal. Appl. 386 (2012), 103–109.
  • M. Brešar and M. Fošner, On rings with involution equipped with some new product, Publ. Math. Debrecen 57 (2000), 121–134.
  • J.-L. Cui and C.-K. Li, Maps preserving product XY −Y X∗ on factor von Neumann algebras, Linear Algebra Appl. 431 (2009), 833–842.
  • L.-Q. Dai and F.-Y. Lu, Nonlinear maps preserving Jordan ∗-products, J. Math. Anal. Appl. 409 (2014), 180–188.
  • M.N. Daif, When is a multiplicative derivation additive? International Journal of Mathematics and Mathematical Sciences 14(3) (1991), 615–618.
  • M. Ferrero and C. Haetinger, Higher derivations of semiprime rings, Comm. Algebra 30 (2002), 2321–2333.
  • A. Fošner, F. Wei, and Z.-K. Xiao, Nonlinear Lie-type derivations of von Neumann algebras and related topics, Colloq. Math. 132 (2013), 53–71.
  • D.-H. Huo, B.-D. Zheng, and H.-Y. Liu, Nonlinear maps preserving Jordan triple τ --products, J. Math. Anal. Appl. 430 (2015), 830–844.
  • D. -H. Huo, B.-D. Zheng, J. -L. Xu, and H.-Y. Liu, Nonlinear mappings preserving Jordan multiple ∗-product on factor von Neumann algebras, Linear Multilinear Algebra 63 (2015), 1026–1036.
  • W. Jing, Nonlinear ∗-Lie derivations of standard operator algebras, Quaestiones Mathematicae 39(8) (2016), 1037–1046.
  • C.-J. Li and F.-Y. Lu, Nonlinear maps preserving the Jordan triple 1-∗-product on von Neumann algebras, Complex Anal. Oper. Theory 11 (2017), 109–117.
  • C.-J. Li, F.-Y. Lu, and X.-C. Fang, Nonlinear mappings preserving product XY + Y X∗ on factor von Neumann algebras, Linear Algebra Appl. 438 (2013), 2339–2345.
  • C.-J. Li, F.-Y. Lu, and X.-C. Fang, Nonlinear ξ-Jordan ∗-derivations on von Neumann algebras, Linear Multilinear Algebra 62 (2014), 466–473.
  • C.-J. Li, F.-Y. Lu, and T. Wang, Nonlinear maps preserving the Jordan triple ∗-product on von Neumann algebras, Ann. Funct. Anal. 7 (2016), 496–507.
  • C.-J. Li, F.-F. Zhao, and Q.-Y. Chen, Nonlinear skew Lie triple derivations between factors, Acta Math. Sinica (English Series) 32 (2016), 821–830.
  • W.-H. Lin, Nonlinear ∗-Lie-type derivations on standard operator algebras, Acta Math. Hungar. 154 (2018), 480–500.
  • W.-H. Lin, Nonlinear ∗-Lie-type derivations on von Neumann algebras, Acta Math. Hungar. https://doi.org/10.1007/s10474-018-0803-1.
  • W.-H. Lin, Nonlinear ∗-Jordan-type derivations on von Neumann algebras, https://arxiv.org/submit/2248854 arXiv: 1805.16027v1 [math.OA].
  • W.-H. Lin, Nonlinear mappings preserving Jordan-type η-∗-products on von Neumann algebras, https://arxiv.org/submit/2248854 arXiv: 1805.96815v1 [math.OA].
  • W.S. Martindale III, When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21 (1969), 695–698.
  • C.R. Mires, Lie homomorphisms of operator algebras, Pacific J. Math. 38 (1971), 717–735.
  • L. Molnár, A condition for a subspace of B(H) to be an ideal, Linear Algebra Appl. 235 (1996), 229–234.
  • L. Molnár, Jordan ∗-derivation pairs on a complex ∗-algebra, Aequationes Math. 54 (1997), 44–55.
  • L. Molnár, Jordan maps on standard operator algebras, In: Functional Equations – Results and Advances, Z. Daróczy and Zs. Páles, (eds.), pp. 305–320, Kluwer Academic Publishers, Dordrecht, 2001.
  • L. Molnár, Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators, Studia Math. 173 (2006), 39–48.
  • L. Molnár and P. Šemrl, Local Jordan ∗-derivations of standard operator algebras, Proc. Amer. Math. Soc. 125 (1997), 447–454.
  • A. Nowicki, Inner derivations of higher orders, Tsukuba J. Math. 8(2) (1984), 219–225.
  • X.-F. Qi and J.-C. Hou, Lie higher derivations on nest algebras, Commun. Math. Res. 26(2) (2010), 131–143.
  • P. Šemrl, Quadratic and quasi-quadratic functionals, Proc. Amer. Math. Soc. 119 (1993), 1105–1113.
  • P. Šemrl, Jordan ∗-derivations of standard operator algebras, Proc. Amer. Math. Soc. 120 (1994), 515–518.
  • A. Taghavi, H. Rohi, and V. Darvish, Non-linear ∗-Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), 426–439.
  • F. Wei and Z.-K. Xiao, Higher derivations of triangular algebras and its generalizations, Linear Algebra Appl. 435 (2011), 1034–1054.
  • Z.-K. Xiao and F. Wei, Nonlinear Lie higher derivations on triangular algebras, Linear Multilinear Algebra 60(8) (2012), 979–994.
  • W.-Y. Yu and J.-H. Zhang, Nonlinear ∗-Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012), 1979–1991.
  • F.-J. Zhang, Nonlinear skew Jordan derivable maps on factor von Neumann algebras, Linear Multilinear Algebra 64 (2016), 2090–2103.
  • F.-J Zhang, X. Qi, and J.-H Zhang, Nonlinear ∗-Lie higher derivations on factor von Neumann algebras, Bull. Iranian Math. Soc. 42(3) (2016), 659–678.
  • F.-J Zhang and J.-H Zhang, Nonlinear Lie derivations on factor von Neumann algebras, Acta Mathematica Sinica. (Chin. Ser) 54(5) (2011), 791–802.
  • F.-F. Zhao and C.-J. Li, Nonlinear ∗-Jordan triple derivations on von Neumann algebras, Math. Slovaca 68 (2018), 163–170.
  • F.-F. Zhao and C.-J. Li, Nonlinear maps preserving the Jordan triple ∗-product between factors, Indag. Math. 29 (2018), 619–627.

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