Nonlinear maps preserving Lie products on triangular algebras

Weiyan Yu

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 56-66
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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Weiyan Yu. "Nonlinear maps preserving Lie products on triangular algebras." Special Matrices 4.1 (2016): 56-66. <http://eudml.org/doc/276901>.

@article{WeiyanYu2016,
abstract = {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.},
author = {Weiyan Yu},
journal = {Special Matrices},
keywords = {Preserver; Lie product; Triangular algebra; Nest algebra; preserver; triangular algebra; nest algebra},
language = {eng},
number = {1},
pages = {56-66},
title = {Nonlinear maps preserving Lie products on triangular algebras},
url = {http://eudml.org/doc/276901},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Weiyan Yu
TI - Nonlinear maps preserving Lie products on triangular algebras
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 56
EP - 66
AB - 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.
LA - eng
KW - Preserver; Lie product; Triangular algebra; Nest algebra; preserver; triangular algebra; nest algebra
UR - http://eudml.org/doc/276901
ER -

References

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  1. [1] M. Brešar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993) 525-546. Zbl0791.16028
  2. [2] D. Benkovič, D. Eremita, Commuting traces and commutativity preserving maps on triangular algebras, J. Algebra, 280 (2004) 797-824.[WoS] Zbl1076.16032
  3. [3] D. Benkovič, Biderivations triangular algebras, Linear Algebra Appl. 431 (2009) 1587-1602. Zbl1185.16045
  4. [4] M. Brešar, P. Šemrl, Commutativity preserving linear maps on central simple algebras, J. Algebras, 284 (2005) 102-110. 
  5. [5] M. Choi, A. Jafarian, H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987) 227-241. Zbl0615.15004
  6. [6] W.S. Cheung, Commuting maps of triangular algebras, J. London math. Soc. 63 (2001) 117-127. Zbl1014.16035
  7. [7] W.S. Cheung, Lie derivation of triangular algebras, Linear Multilinear Algebra, 51 (2003) 299-310. Zbl1060.16033
  8. [8] K.R. Davidson, Nest algebras, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, 1988. Zbl0669.47024
  9. [9] J.C. Hou, M.Y. Jiao, Additive maps preserving Jordan zero-products on nest algebras, Linear Algebra Appl. 429 (2008) 190-208.[WoS] Zbl1140.47028
  10. [10] F.Y. Lu, Additive Jordan isomorphisms of nest algebras on normed spaces, J. Math. Anal. Appl. 284 (2003) 127-143. Zbl1032.46064
  11. [11] L.W. Marcoux, Lie isomorphisms of nest algebras, J. Funct. Anal. Appl. 164 (1999) 163-180.[WoS] Zbl0940.47061
  12. [12] W.S. Martindale, Lie isomorphisms of simple rings, J. London Math. Soc. 44 (1969) 213-221. Zbl0164.03901
  13. [13] C.R. Miers, Commutativity preserving maps of factors, Canad. J. Math. 40 (1988) 248-256. Zbl0632.46055
  14. [14] C.R. Miers, Lie isomorphisms of operator algebras, Pacific J. Math. 38 (1971) 717-735. Zbl0204.14803
  15. [15] C.R. Miers, Lie isomorphisms of factors, Trans. Amer. Math. Soc. 147 (1970) 55-63. Zbl0191.42901
  16. [16] L. Molnár, P. Šemrl, Nonlinear commutativity preserving maps on self-adjoint operators, Q. J. Math. 56 (2005) 589-595. 
  17. [17] M. Omladič, H. Radjavi, P. Šemrl, Preserving commutativity, J. Pure Appl. Algebra 156 (2001) 309-328. 
  18. [18] P. Šemrl, Non-linear commutativity preserving maps, Acta Sci. Math. (Szeged) 71 (2005) 781-819. Zbl1111.15002
  19. [19] T.L. Wong, Jordan isomorphisms of triangular algebras, Linear Algebra Appl. 418 (2006) 225-233. 
  20. [20] J.H. Zhang, W.Y. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006) 251-255. Zbl1103.47026
  21. [21] W.Y. YU, J.H. Zhang, Nonlinear Lie derivations of triangular algebras, Linear Algebra Appl. 432 (2010) 2953-2960. Zbl1193.16030
  22. [22] W.Y. YU, J.H. Zhang, Lie triple derivations of CSL algebras, Int Theor Phys. 52 (2013) 2118-2127. Zbl1270.81015
  23. [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] Zbl1178.47024
  24. [24] W.Y. YU, J.H. Zhang, Nonlinear *-Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012) 1979-1991.[WoS] Zbl1263.46058

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