Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
80-100
Opis fizyczny
Daty
otrzymano
2015-07-08
zaakceptowano
2015-12-13
online
2016-01-20
Twórcy
autor
- Fošner, University of Primorska, Faculty of Management, Cankarjeva 5, SI-6000 Koper, Slovenia
autor
- University of Primorska, FAMNIT, Glagoljaška 8, SI-6000 Koper and Institute of Mathematics, Physics and Mechanics, Department of Mathematics, Jadranska 19, SI-1000 Ljubljana, Slovenia
Bibliografia
- [1] R. Bhatia, P. Rosenthal, How and why to solve the operator equation AX − XB = Y, Bull. London Math. Soc. 29 (1997), 1–21.
- [2] M. Brešar, Commuting traces of biadditive mappings, commutativity preserving mappings, and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525–546.
- [3] M. Brešar, C. R. Miers, Commutativity preserving mappings of von Neumann algebras, Canad. J. Math. 45 (1993), 695–708.
- [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.
- [5] M. D. Choi, A. Jafarian, H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227–241. [WoS]
- [6] J. Cui, J. Hou, Maps leaving functional values of operator products invariant, Linear Algebra Appl. 428 (2008), 1649–1663. [WoS]
- [7] C.-A. Faure, An elementary proof of the fundamental theorem of projective geometry, Geom. Dedicata 90 (2002), 145–151.
- [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.
- [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. [WoS]
- [10] W. Fulton, Algebraic topology: a first course, Springer, Graduate Texts in Mathematics 153, New York (1995).
- [11] F. R. Gantmacher, Applications of the theory of matrices, Interscience Publishers, Inc., New York (1959).
- [12] R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge University Press, Cambridge (1985).
- [13] C.-K. Li, S. Pierce, Linear preserver problems, Amer. Math. Monthly 108 (2001), 591–605.
- [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.
- [15] G. Lumer, M. Rosenblum, Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32–41.
- [16] L. Molnár, Selected preserver problems on algebraic structures of linear operators and on function spaces, Springer, Lecture Notes in Mathematics 1895, Berlin (2007).
- [17] L. Molnár, P. Šemrl, Nonlinear commutativity preserving maps on self-adjoint operators, Q. J. Math. 56 (2005), 589–595.
- [18] M. Omladič, H. Radjavi, P. Šemrl, Preserving commutativity, J. Pure Appl. Algebra 156 (2001), 309–328.
- [19] T. Petek, Additive mappings preserving commutativity, Linear Multilinear Algebra 42 (1997), 205–211. [Crossref][WoS]
- [20] T. Petek, Mappings preserving spectrum and commutativity on Hermitian matrices, Linear Algebra Appl. 290 (1999), 167– 191.
- [21] T. Petek, A note on additive commutativity-preserving mappings, Publ. Math. (Debr.) 56 (2000), 53–61.
- [22] T. Petek, H. Sarria, Spectrum and commutativity preserving mappings on H2, Linear Algebra Appl. 364 (2003), 317–319.
- [23] T. Petek, P. Šemrl, Adjacency preserving maps on matrices and operators, Proc. R. Soc. Edinb. 132 (2002), 661–684.
- [24] S. Pierce et.al., A survey of linear preserver problems, Linear Multilinear Algebra 33 (1992), 1–192.
- [25] P. Šemrl, Non-linear commutativity preserving maps, Acta Sci. Math. (Szeged) 71 (2005), 781–819.
- [26] P. Šemrl, Commutativity preserving maps, Linear Algebra Appl. 429 (2008), 1051–1070. [WoS]
- [27] W. Watkins, Linear maps that preserve commuting pairs of matrices, Linear Algebra Appl. 14 (1976), 29–35.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0009