Table of Contents Author Guidelines Submit a Manuscript
Journal of Mathematics
Volume 2015 (2015), Article ID 428203, 6 pages
http://dx.doi.org/10.1155/2015/428203
Research Article

Maps Preserving Idempotence on Matrix Spaces

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 5 July 2015; Accepted 30 August 2015

Academic Editor: Fernando Torres

Copyright © 2015 Yuqiu Sheng and Hanyu Zhang. 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. A. Bourhim, M. Burgos, and V. S. Shulman, “Linear maps preserving the minimum and reduced minimum moduli,” Journal of Functional Analysis, vol. 258, no. 1, pp. 50–66, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. G. Dolinar, “Maps on matrix algebras preserving idempotents,” Linear Algebra and its Applications, vol. 371, pp. 287–300, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  3. C.-K. Li and S. Pierce, “Linear preserver problems,” The American Mathematical Monthly, vol. 108, no. 7, pp. 591–605, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. Šemrl, “Order-preserving maps on the poset of idempotent matrices,” Acta Scientiarum Mathematicarum, vol. 69, no. 3-4, pp. 481–490, 2003. View at Google Scholar · View at MathSciNet
  5. P. Šemrl, “Hua's fundamental theorems of the geometry of matrices and related results,” Linear Algebra and its Applications, vol. 361, pp. 161–179, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. W. Liu and D. B. Zhao, Introduction to Linear Preserver Problems, Harbin Press, Harbin, China, 1997.
  7. X. Zhang, “Idempotence-preserving maps without the linearity and surjectivity assumptions,” Linear Algebra and its Applications, vol. 387, pp. 167–182, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Q. Sheng, B. D. Zheng, and X. Zhang, “Maps on spaces of symmetric matrices preserving idempotence,” Linear Algebra and Its Applications, vol. 420, no. 2-3, pp. 576–585, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. Q. Sheng, B. D. Zheng, and X. Zhang, “Idempotence preserving maps on spaces of triangular matrices,” Journal of Applied Mathematics & Computing, vol. 25, no. 1-2, pp. 17–33, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus