Preserving zeros of Lie product on alternate matrices

References

[1] R. Bhatia, P. Rosenthal, How and why to solve the operator equation AX − XB = Y, Bull. London Math. Soc. 29 (1997), 1–21. 10.1112/S0024609396001828Search in Google Scholar

[2] M. Brešar, Commuting traces of biadditive mappings, commutativity preserving mappings, and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525–546. 10.1090/S0002-9947-1993-1069746-XSearch in Google Scholar

[3] M. Brešar, C. R. Miers, Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), 695–708. 10.4153/CJM-1993-039-xSearch in Google Scholar

[4] J.-T. Chan, C.-K. Li, N.-S. Sze, Mappings on matrices: invariance of functional values of matrix products, J. Aust. Math. Soc. 81 (2006), 165–184. 10.1017/S1446788700015809Search in Google Scholar

[5] M. D. Choi, A. Jafarian, H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227–241. 10.1016/0024-3795(87)90169-8Search in Google Scholar

[6] J. Cui, J. Hou, Maps leaving functional values of operator products invariant, Linear Algebra Appl. 428 (2008), 1649–1663. 10.1016/j.laa.2007.10.010Search in Google Scholar

[7] C.-A. Faure, An elementary proof of the fundamental theorem of projective geometry, Geom. Dedicata 90 (2002), 145–151. 10.1023/A:1014933313332Search in Google Scholar

[8] P.A. Fillmore, D.A. Herrero, W.E. Longstaff, The hyperinvariant subspace lattice of a linear transformation, Linear Algebra Appl. 17 (1977), 125–132. 10.1016/0024-3795(77)90032-5Search in Google Scholar

[9] A. Fošner, B. Kuzma, T. Kuzma, N.-S. Sze, Maps preserving matrix pairs with zero Jordan product, Linear Multilinear Algebra 59 (2011), 507–529. 10.1080/03081081003600463Search in Google Scholar

[10] W. Fulton, Algebraic topology: a first course, Springer, Graduate Texts in Mathematics 153, New York (1995). Search in Google Scholar

[11] F. R. Gantmacher, Applications of the theory of matrices, Interscience Publishers, Inc., New York (1959). Search in Google Scholar

[12] R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge University Press, Cambridge (1985). 10.1017/CBO9780511810817Search in Google Scholar

[13] C.-K. Li, S. Pierce, Linear preserver problems, Amer. Math. Monthly 108 (2001), 591–605. 10.1080/00029890.2001.11919790Search in Google Scholar

[14] C.-K. Li, N.-K. Tsing, Linear preserver problems: A brief introduction and some special techniques, Linear Algebra Appl. 162- 164 (1992), 217–235. Search in Google Scholar

[15] G. Lumer, M. Rosenblum, Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32–41. 10.1090/S0002-9939-1959-0104167-0Search in Google Scholar

[16] L. Molnár, Selected preserver problems on algebraic structures of linear operators and on function spaces, Springer, Lecture Notes in Mathematics 1895, Berlin (2007). Search in Google Scholar

[17] L. Molnár, P. Šemrl, Nonlinear commutativity preserving maps on self-adjoint operators, Q. J. Math. 56 (2005), 589–595. 10.1093/qmath/hah058Search in Google Scholar

[18] M. Omladič, H. Radjavi, P. Šemrl, Preserving commutativity, J. Pure Appl. Algebra 156 (2001), 309–328. 10.1016/S0022-4049(99)00154-1Search in Google Scholar

[19] T. Petek, Additive mappings preserving commutativity, Linear Multilinear Algebra 42 (1997), 205–211. 10.1080/03081089708818499Search in Google Scholar

[20] T. Petek, Mappings preserving spectrum and commutativity on Hermitian matrices, Linear Algebra Appl. 290 (1999), 167– 191. 10.1016/S0024-3795(98)10225-2Search in Google Scholar

[21] T. Petek, A note on additive commutativity-preserving mappings, Publ. Math. (Debr.) 56 (2000), 53–61. 10.5486/PMD.2000.2111Search in Google Scholar

[22] T. Petek, H. Sarria, Spectrum and commutativity preserving mappings on H2, Linear Algebra Appl. 364 (2003), 317–319. 10.1016/S0024-3795(02)00585-2Search in Google Scholar

[23] T. Petek, P. Šemrl, Adjacency preserving maps on matrices and operators, Proc. R. Soc. Edinb. 132 (2002), 661–684. 10.1017/S0308210500001839Search in Google Scholar

[24] S. Pierce et.al., A survey of linear preserver problems, Linear Multilinear Algebra 33 (1992), 1–192. 10.1080/03081089208818176Search in Google Scholar

[25] P. Šemrl, Non-linear commutativity preserving maps, Acta Sci. Math. (Szeged) 71 (2005), 781–819. Search in Google Scholar

[26] P. Šemrl, Commutativity preserving maps, Linear Algebra Appl. 429 (2008), 1051–1070. 10.1016/j.laa.2007.05.006Search in Google Scholar

[27] W. Watkins, Linear maps that preserve commuting pairs of matrices, Linear Algebra Appl. 14 (1976), 29–35. 10.1016/0024-3795(76)90060-4Search in Google Scholar