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Articles

Multiplicative *-Lie type higher derivations of standard operator algebras

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Pages 3777-3797 | Received 01 Aug 2019, Accepted 06 Feb 2021, Published online: 10 May 2021

References

  • An, R.-L., Hou, J.-C. (2010). A characterization of *-automorphism on B(H). Acta. Math. Sinica (English Series). 26:287–294.
  • Ashraf, M., Parveen, N. (2016). On Jordan triple higher derivable mappings in rings. Mediterr. J. Math. 13(4):1465–1477. DOI: 10.1007/s00009-015-0606-3.
  • Ashraf, M., Parveen, N. (2017). Lie triple higher derivable maps on rings. Commun. Algebra 45(5):2256–2275. DOI: 10.1080/00927872.2016.1233195.
  • Ashraf, M., Wani, B. A. (2018). Multiplicative Lie triple higher derivations on standard operator algebras, Math. Reports. (To appear).
  • Ashraf, M., Wani, B. A., Wei, F. (in press). Multiplicative *-Lie triple higher derivations of standard operator algebras. Quaest. Math. DOI: 10.2989/16073606.2018.1502213.
  • Bai, Z.-F., Du, S.-P. (2012). Maps preserving products XY−YX∗ on von Neumann algebras. J. Math. Anal. Appl. 386:103–109.
  • Brešar, M., Fošner, M. (2000). On rings with involution equipped with some new product. Publ. Math. Debrecen. 57:121–134.
  • Cui, J.-L., Li, C.-K. (2009). Maps preserving product XY−YX∗ on factor von Neumann algebras. Linear Algebra Appl. 431:833–842.
  • Daif, M. N. (1991). When is a multiplicative derivation additive? Int. J. Math. Sci. 14(3):615–618. DOI: 10.1155/S0161171291000844.
  • Dai, L.-Q., Lu, F.-Y. (2014). Nonlinear maps preserving Jordan *-products. J. Math. Anal. Appl. 409(1):180–188. DOI: 10.1016/j.jmaa.2013.07.019.
  • Ferrero, M., Haetinger, C. (2002). Higher derivations of semiprime rings. Commun. Algebra 30(5):2321–2333. DOI: 10.1081/AGB-120003471.
  • Fošner, A., Wei, F., Xiao, Z.-K. (2013). Nonlinear Lie-type derivations of von Neumann algebras and related topics. Colloq. Math. 132(1):53–71. DOI: 10.4064/cm132-1-5.
  • Huo, D.-H., Zheng, B.-D., Liu, H.-Y. (2015). Nonlinear maps preserving Jordan triple τ-*-products. J. Math. Anal. Appl. 430(2):830–844. DOI: 10.1016/j.jmaa.2015.05.021.
  • Huo, D.-H., Zheng, B.-D., Xu, J.-L., Liu, H.-Y. (2015). Nonlinear mappings pre- serving Jordan multiple *-product on factor von Neumann algebras. Linear Multilinear Algebra 63(5):1026–1036. DOI: 10.1080/03081087.2014.915321.
  • Jing, W. (2016). Nonlinear *-Lie derivations of standard operator algebras. Quaest. Math. 39(8):1037–1046. DOI: 10.2989/16073606.2016.1247119.
  • Li, C.-J., Zhao, F.-F., Chen, Q.-Y. (2016). Nonlinear skew Lie triple derivations between factors. Acta Math. Sin-English. Ser. 32(7):821–830. DOI: 10.1007/s10114-016-5690-1.
  • Lin, W.-H. (2018). Nonlinear *-Lie-type derivations on standard operator algebras. Acta Math. Hungar. 154(2):480–500. DOI: 10.1007/s10474-017-0783-6.
  • Lin, W.-H. (2018). Nonlinear *-Lie-type derivations on von Neumann algebras. Acta Math. Hungar. 156(1):112–131. DOI: 10.1007/s10474-018-0803-1.
  • Martindale, W. S. III, (1969). When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21(3):695–698. DOI: 10.1090/S0002-9939-1969-0240129-7.
  • Mires, C. R. (1971). Lie homomorphisms of operator algebras. Pacific J. Math. 38:717–735.
  • Molnár, L. (1996). A condition for a subspace of B(H) to be an ideal. Linear Algebra Appl. 235:229–234.
  • Molnár, L. (1997). Jordan *-derivation pairs on a complex *-algebra. Aequ. Math. 54(1-2):44–55. DOI: 10.1007/BF02755445.
  • Molnár, L. (2002). Jordan maps on standard operator algebras. In: Daróczy, Z., Páles, Z., eds. Functional Equations—Results and Advances. Boston, MA: Springer, p. 305–320.
  • Nowicki, A. (1984). Inner derivations of higher orders. Tsukuba J. Math. 8(2):219–225. DOI: 10.21099/tkbjm/1496160039.
  • Qi, X.-F., Hou, J.-C. (2010). Lie higher derivations on nest algebras. Commun. Math. Res. 26:131–143.
  • Šemrl, P. (1991). Additive derivations of some operator algebras. Llinois J. Math. 35:234–240.
  • Šemrl, P. (1993). Quadratic and quasi-quadratic functionals. Proc. Amer. Math. Soc. 119(4):1105–1113. DOI: 10.1090/S0002-9939-1993-1158008-3.
  • Wei, F., Xiao, Z.-K. (2011). Higher derivations of triangular algebras and its generalizations. Linear Algebra Appl. 435(5):1034–1054. DOI: 10.1016/j.laa.2011.02.027.
  • Xiao, Z.-K., Wei, F. (2012). Nonlinear Lie higher derivations on triangular algebras. Linear Multilinear Algebra 60(8):979–994. DOI: 10.1080/03081087.2011.639373.
  • Yu, W.-Y., Zhang, J.-H. (2012). Nonlinear *-Lie derivations on factor von Neumann algebras. Linear Algebra Appl. 437(8):1979–1991. DOI: 10.1016/j.laa.2012.05.032.
  • Zhang, F.-J., Qi, X.-F., Zhang, J.-H. (2016). Nonlinear *-Lie higher derivations on factor von Neumann algebras, Bull. Iranian Math. Soc. 42:659–678.
  • Zhang, F.-J., Zhang, J.-H. (2011). Nonlinear Lie derivations on factor von Neumann algebras, Acta Mathematica Sinica. Chinese Series. 54:791–802.
  • Zhao, F.-F., Li, C.-J. (2018). Nonlinear *-Jordan triple derivations on von Neumann algebras. Math. Slovaca. 68(1):163–170. DOI: 10.1515/ms-2017-0089.
  • Zhao, F.-F., Li, C.-J. (2018). Nonlinear maps preserving the Jordan triple *-product between factors. Indag. Math. 29(2):619–627. DOI: 10.1016/j.indag.2017.10.010.

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