`ISRN Applied MathematicsVolume 2012 (2012), Article ID 251389, 13 pageshttp://dx.doi.org/10.5402/2012/251389`
Research Article

## Maps Completely Preserving Involutions and Maps Completely Preserving Drazin Inverse

1College of Science, Harbin Engineering University, Harbin 150001, China
2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
3East University of Heilongjiang, Harbin 150001, China

Received 24 August 2012; Accepted 2 October 2012

Academic Editors: H. Y. Chung and H. A. Larrondo

Copyright © 2012 Hongmei Yao 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.

1. J. C. Hou and J. L. Cui, Introduction to the Linear Maps on Operator Algebras, Scinece press, Beijing, China, 2002.
2. L. Yang and L. Zhang, “Maps on $B\left(H\right)$ preserving involution,” Linear Algebra and its Applications, vol. 431, no. 5–7, pp. 666–672, 2009.
3. J. Cui, “Additive drazin inverse preservers,” Linear Algebra and its Applications, vol. 426, no. 2-3, pp. 448–453, 2007.
4. E. G. Effros and Z.-J. Ruan, Operator Spaces, The Clarendon Press, Oxford, UK, 2000.
5. D. Hadwin and D. R. Larson, “Completely rank-nonincreasing linear maps,” Journal of Functional Analysis, vol. 199, no. 1, pp. 210–227, 2003.
6. J. Hou and L. Huang, “Characterizing isomorphisms in terms of completely preserving invertibility or spectrum,” Journal of Mathematical Analysis and Applications, vol. 359, no. 1, pp. 81–87, 2009.
7. J. Cui and J. Hou, “Linear maps on von Neumann algebras preserving zero products or TR-rank,” Bulletin of the Australian Mathematical Society, vol. 65, no. 1, pp. 79–91, 2002.
8. J. L. Cui and J. C. Hou, “A characterization of homomorphisms between Banach algebras,” Acta Mathematica Sinica, vol. 20, no. 4, pp. 761–768, 2004.
9. L. Huang and J. Hou, “Maps completely preserving spectral functions,” Linear Algebra and Its Applications, vol. 435, no. 11, pp. 2756–2765, 2011.
10. J. Hou and L. Huang, “Maps completely preserving idempotents and maps completely preserving square-zero operators,” Israel Journal of Mathematics, vol. 176, pp. 363–380, 2010.
11. X. Liu, L. L. Wu, and J. Benítez, “On linear combinations of generalized involutive matrices,” Linear and Multilinear Algebra, vol. 59, no. 11, pp. 1221–1236, 2011.