Maps preserving the square zero of ?-Lie product of operators

• Taghavi, Ali ^[1] ; Hosseinzadeh, Roja ^[1] ; Yousefi, Masoomeh ^[1]
  1. [1] University of Mazandaran

     University of Mazandaran

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 3, 2020, págs. 591-597
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2020-03-0036
• Enlaces
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• Resumen

  • Let B(H) be the algebra of all bounded linear operators on an infinite dimensional Hilbert space ?. In this paper, we identify the form of the unital surjective additive map ? : B(H)? B(H)which preserves the square zero of ?-Lie product of operators for some scalar ? with ? ? 0, 1, ?1.

• Referencias bibliográficas
  • M. A. Chebotar, W.-F. Ke, P.-H. Lee, and N.-C. Wong, “Mappings preserving zero products”, Studia mathematica, vol. 155, no. 1, pp. 77–94,...
  • M. Dobovišek, B. Kuzma, G. Lešnjak, C. Li, and T. Petek, “Mappings that preserve pairs of operators with zero triple Jordan product”, Linear...
  • G. Dolinar, S. Du, J. Hou, and P. Legiša, “General preservers of invariant subspace lattices”, Linear algebra and its applications, vol. 429,...
  • L. Fang, G. Ji, and Y. Pang, “Maps preserving the idempotency of products of operators”, Linear algebra and its applications, vol. 426, no....
  • J. Hou and L. Huang, “Maps completely preserving idempotents and maps completely preserving square-zero operators”, Israel journal of mathematics,...
  • L. Molnár, “Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators”, Studia mathematica, vol. 173, no. 1, pp....
  • P. Šemrl, “Linear mappings that preserve operators annihilated by a polynomial”, Journal of operator theory, 36, pp. 45-58, 1996. [On line]....
  • A. Taghavi and R. Hosseinzadeh, “Maps preserving the dimension of fixed points of products of operators”, Linear and multilinear algebra,...
  • A. Taghavi, R. Hosseinzadeh, and H. Rohi, “Maps preserving the fixed points of sum of operators”, Operators and matrices, no. 3, pp. 563–569,...
  • A. Taghavi, F. Kolivand, and H. Rohi, “A note on strong η-Lie products preserving maps on some algebras”, Mediterranean journal of mathematics,...
  • M. Wang, L. Fang, and G. Ji, “Linear maps preserving idempotency of products or triple jordan products of operators”, Linear algebra and its...
  • J.-H. Zhang and F.-J. Zhang, “Nonlinear maps preserving Lie products on factor von Neumann algebras”, Linear algebra and its applications,...