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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 104272, 9 pages
http://dx.doi.org/10.1155/2014/104272
Research Article

Characterizing -Lie Multiplicative Isomorphisms on Von Neumann Algebras

1Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
2Department of Mathematics, Shanxi University, Taiyuan 030006, China

Received 1 September 2013; Revised 1 December 2013; Accepted 12 December 2013; Published 23 January 2014

Academic Editor: Chi-Keung Ng

Copyright © 2014 Yamin Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. S. Martindale, III, “When are multiplicative mappings additive?” Proceedings of the American Mathematical Society, vol. 21, pp. 695–698, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. An and J. Hou, “Additivity of Jordan multiplicative maps on Jordan operator algebras,” Taiwanese Journal of Mathematics, vol. 10, no. 1, pp. 45–64, 2006. View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. F. Lu, “Multiplicative mappings of operator algebras,” Linear Algebra and its Applications, vol. 347, pp. 283–291, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Bai, S. Du, and J. Hou, “Multiplicative lie isomorphisms between prime rings,” Communications in Algebra, vol. 36, no. 5, pp. 1626–1633, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. X. Qi and J. Hou, “Additivity of Lie multiplicative maps on triangular algebras,” Linear and Multilinear Algebra, vol. 59, no. 4, pp. 391–397, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. X. Qi and J. Hou, “Characterization of Lie multiplicative isomorphisms between nest algebras,” Science China Mathematics, vol. 54, no. 11, pp. 2453–2462, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. J. A. Brooke, P. Busch, and D. B. Pearson, “Commutativity up to a factor of bounded operators in complex Hilbert space,” Proceedings of the Royal Society: Series A, vol. 458, no. 2017, pp. 109–118, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Kassel, Quantum Groups, vol. 155 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  9. X. Qi and J. Hou, “Additive Lie (ξ-Lie) derivations and generalized Lie (ξ-Lie) derivations on nest algebras,” Linear Algebra and Its Applications, vol. 431, no. 5–7, pp. 843–854, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. X. Qi and J. Hou, “Characterization of ξ-Lie multiplicative isomorphisms,” Operators and Matrices, vol. 4, no. 3, pp. 417–429, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Aczél and J. Dhombres, Functional Equations in Several Variables, vol. 31 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, UK, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Dixmier, Von Neumann Algebras, vol. 27 of North-Holland Mathematical Library, North-Holland, Amsterdam, The Netherlands, 1981. View at MathSciNet
  13. C. R. Miers, “Lie homomorphisms of operator algebras,” Pacific Journal of Mathematics, vol. 38, pp. 717–735, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Brešar and C. R. Miers, “Commutativity preserving mappings of von Neumann algebras,” Canadian Journal of Mathematics, vol. 45, no. 4, pp. 695–708, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Brešar, “Jordan mappings of semiprime rings II,” Bulletin of the Australian Mathematical Society, vol. 44, no. 2, pp. 233–238, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet