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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 148321, 8 pages
Linear Maps on Upper Triangular Matrices Spaces Preserving Idempotent Tensor Products
1Department of Foundation, Harbin Finance University, Harbin 150030, China
2School of Mathematical Science, Heilongjiang University, Harbin 150080, China
3Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Received 26 October 2013; Accepted 10 December 2013; Published 28 January 2014
Academic Editor: Antonio M. Peralta
Copyright © 2014 Li Yang 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.
- C.-K. Li and S. Pierce, “Linear preserver problems,” The American Mathematical Monthly, vol. 108, no. 7, pp. 591–605, 2001.
- L. Molnár, Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, vol. 1895 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2007.
- G. H. Chan, M. H. Lim, and K.-K. Tan, “Linear preservers on matrices,” Linear Algebra and Its Applications, vol. 93, pp. 67–80, 1987.
- P. Šemrl, “Applying projective geometry to transformations on rank one idempotents,” Journal of Functional Analysis, vol. 210, no. 1, pp. 248–257, 2004.
- X. M. Tang, C. G. Cao, and X. Zhang, “Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings,” Linear Algebra and its Applications, vol. 338, pp. 145–152, 2001.
- N. Jacobson, Lectures in Abstract Algebra, vol. 2, D. van Nostrand, Toronto, Canada, 1953.
- T. Oikhberg and A. M. Peralta, “Automatic continuity of orthogonality preservers on a non-commutative space,” Journal of Functional Analysis, vol. 264, no. 8, pp. 1848–1872, 2013.
- M. A. Chebotar, W.-F. Ke, P.-H. Lee, and N.-C. Wong, “Mappings preserving zero products,” Studia Mathematica, vol. 155, no. 1, pp. 77–94, 2003.
- C.-W. Leung, C.-K. Ng, and N.-C. Wong, “Linear orthogonality preservers of Hilbert -modules over -algebras with real rank zero,” Proceedings of the American Mathematical Society, vol. 140, no. 9, pp. 3151–3160, 2012.
- I. V. Konnov and J. C. Yao, “On the generalized vector variational inequality problem,” Journal of Mathematical Analysis and Applications, vol. 206, no. 1, pp. 42–58, 1997.
- D. Huo, B. Zheng, and H. Liu, “Characterizations of nonlinear Lie derivations of ,” Abstract and Applied Analysis, vol. 2013, Article ID 245452, 7 pages, 2013.
- H. Yao and B. Zheng, “Zero triple product determined matrix algebras,” Journal of Applied Mathematics, vol. 2012, Article ID 925092, 18 pages, 2012.
- J. Xu, B. Zheng, and L. Yang, “The automorphism group of the Lie ring of real skew-symmetric matrices,” Abstract and Applied Analysis, vol. 2013, Article ID 638230, 8 pages, 2013.
- X. Song, C. Cao, and B. Zheng, “A note on -potence preservers on matrix spaces over complex field,” Abstract and Applied Analysis, vol. 2013, Article ID 581683, 8 pages, 2013.
- A. Fosner, Z. Haung, C. K. Li, and N. S. Sze, “Linear preservers and quantum information science,” Linear and Multilinear Algebra, vol. 61, no. 10, pp. 1377–1390, 2013.
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK, 2000.
- J. Xu, B. Zheng, and H. Yao, “Linear transformations between multipartite quantum systems that map the set of tensor product of idempotent matrices into idempotent matrix set,” Journal of Function Spaces and Applications, vol. 2013, Article ID 182569, 7 pages, 2013.
- B. D. Zheng, J. L. Xu, and A. Fosner, “Linear maps preserving rank of tensor products of matrices,” Linear and Multilinear Algebra. In press.
- J. L. Xu, B. D. Zheng, and C. G. Cao, “A characterization of comparable tableaux,” Submitted to Journal of Combinatorial Theory A.