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2016 | 4 | 1 | 80-100
Tytuł artykułu

Preserving zeros of Lie product on alternate matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
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
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