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2016 | 4 | 1 | 56-66
Tytuł artykułu

Nonlinear maps preserving Lie products on triangular algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
56-66
Opis fizyczny
Daty
wydano
2016-01-01
otrzymano
2015-09-06
zaakceptowano
2015-11-10
online
2015-12-16
Twórcy
autor
  • College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, PR. China, wyyume65@163.com
Bibliografia
  • [1] M. Brešar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993) 525-546.
  • [2] D. Benkovič, D. Eremita, Commuting traces and commutativity preserving maps on triangular algebras, J. Algebra, 280 (2004) 797-824.[WoS]
  • [3] D. Benkovič, Biderivations triangular algebras, Linear Algebra Appl. 431 (2009) 1587-1602.
  • [4] M. Brešar, P. Šemrl, Commutativity preserving linear maps on central simple algebras, J. Algebras, 284 (2005) 102-110.
  • [5] M. Choi, A. Jafarian, H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987) 227-241.
  • [6] W.S. Cheung, Commuting maps of triangular algebras, J. London math. Soc. 63 (2001) 117-127.
  • [7] W.S. Cheung, Lie derivation of triangular algebras, Linear Multilinear Algebra, 51 (2003) 299-310.
  • [8] K.R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, 1988.
  • [9] J.C. Hou, M.Y. Jiao, Additive maps preserving Jordan zero-products on nest algebras, Linear Algebra Appl. 429 (2008) 190-208.[WoS]
  • [10] F.Y. Lu, Additive Jordan isomorphisms of nest algebras on normed spaces, J. Math. Anal. Appl. 284 (2003) 127-143.
  • [11] L.W. Marcoux, Lie isomorphisms of nest algebras, J. Funct. Anal. Appl. 164 (1999) 163-180.[WoS]
  • [12] W.S. Martindale, Lie isomorphisms of simple rings, J. London Math. Soc. 44 (1969) 213-221.
  • [13] C.R. Miers, Commutativity preserving maps of factors, Canad. J. Math. 40 (1988) 248-256.
  • [14] C.R. Miers, Lie isomorphisms of operator algebras, Pacific J. Math. 38 (1971) 717-735.
  • [15] C.R. Miers, Lie isomorphisms of factors, Trans. Amer. Math. Soc. 147 (1970) 55-63.
  • [16] L. Molnár, P. Šemrl, Nonlinear commutativity preserving maps on self-adjoint operators, Q. J. Math. 56 (2005) 589-595.
  • [17] M. Omladič, H. Radjavi, P. Šemrl, Preserving commutativity, J. Pure Appl. Algebra 156 (2001) 309-328.
  • [18] P. Šemrl, Non-linear commutativity preserving maps, Acta Sci. Math. (Szeged) 71 (2005) 781-819.
  • [19] T.L. Wong, Jordan isomorphisms of triangular algebras, Linear Algebra Appl. 418 (2006) 225-233.
  • [20] J.H. Zhang, W.Y. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006) 251-255.
  • [21] W.Y. YU, J.H. Zhang, Nonlinear Lie derivations of triangular algebras, Linear Algebra Appl. 432 (2010) 2953-2960.
  • [22] W.Y. YU, J.H. Zhang, Lie triple derivations of CSL algebras, Int Theor Phys. 52 (2013) 2118-2127.
  • [23] J.H. Zhang, F.J. zhang, Nonlinear maps preserving lie products on factor von Neumann algebras, Linear Algebra Appl. 429 (2008) 18-30.[WoS]
  • [24] W.Y. YU, J.H. Zhang, Nonlinear *-Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012) 1979-1991.[WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0006
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