Linear k-power/k-potent preservers between matrix spaces

Linear Algebra and Its Applications - Tập 412 - Trang 373-379 - 2006
Xian Zhang1, Chong-guang Cao1
1School of Mathematical Science, Heilongjiang University, Harbin 150080, PR China

Tài liệu tham khảo

Brešar, 1993, Linear transformations preserving potent matrices, Proc. Amer. Math. Soc., 119, 81, 10.1090/S0002-9939-1993-1154242-7 Cao, 1999, Linear maps preserving idempotence on matrix modules over some rings, J. Heilongjiang Univ. Natur. Sci., 16, 1 Cao, 2001 Cao, 2005, Linear preservers between matrix modules over connected commutative rings, Linear Algebra Appl., 397, 355, 10.1016/j.laa.2004.11.013 Chan, 1987, Linear preservers on matrices, Linear Algebra Appl., 93, 67, 10.1016/S0024-3795(87)90312-0 Chan, 1992, Linear preservers on powers of matrices, Linear Algebra Appl., 162–164, 615, 10.1016/0024-3795(92)90396-R Cheung, 2003, Linear maps transforming the unitary group, Canad. Math. Bull., 46, 54, 10.4153/CMB-2003-005-8 Cheung, 2004, Isometries between matrix algebras, J. Austral. Math. Soc., 77, 1, 10.1017/S1446788700010119 Gerstenhaber, 1958, On nilalgebras and linear varieties of nilpotent matrices I, Amer. J. Math., 80, 614, 10.2307/2372773 Herstein, 1969 Li, 2005, Isometries for Ky Fan norms between matrix spaces, Proc. Amer. Math. Soc., 133, 369, 10.1090/S0002-9939-04-07510-0 Li, 2005, Linear maps transforming the higher numerical ranges, Linear Algebra Appl., 400, 291, 10.1016/j.laa.2004.11.026 Li, 2004, Linear operators transforming H-unitary matrices, Linear Algebra Appl., 377, 111, 10.1016/j.laa.2003.08.002 Li, 2001, Linear preserver problems, Amer. Math. Monthly, 108, 591, 10.2307/2695268 Li, 2002, Linear transformations between matrix spaces that map one rank specific set into another, Linear Algebra Appl., 357, 197, 10.1016/S0024-3795(02)00381-6 Lim, 1990, Linear mappings on second symmetric product spaces that preserve rank less than or equal to one, Linear and Multilinear Algebra, 26, 187, 10.1080/03081089008817975 Lim, 1975, Linear transformations of tensor spaces preserving decomposable vectors, Publ. Inst. Math. (Beograd) (N.S.), 18, 131 Liu, 1997 Liu, 1997, Linear maps preserving idempotence on matrix modules over principal ideal domains, Linear Algebra Appl., 258, 219, 10.1016/S0024-3795(96)00203-0 Omladič, 1993, Additive mappings preserving operators of rank one, Linear Algebra Appl., 182, 239, 10.1016/0024-3795(93)90502-F Tang, 2003, Linear operators preserving adjoint matrix between matrix spaces, Linear Algebra Appl., 372, 287, 10.1016/S0024-3795(03)00532-9 Tong, 2003, Idempotent preserving linear operators from symmetric matrix spaces to all matrix spaces over fields, J. Heilongjiang Univ. Natur. Sci., 20, 25 Zhang, 2004, Additive maps preserving Moore–Penrose inverses of matrices on symmetric matrix spaces, Linear and Multilinear Algebra, 52, 349, 10.1080/03081080410001667825 Zhang, 2001