Jordan product and fixed points preservers

• Elhodaibi, Mhamed ^[1] ; Elouazzani, Soufiane ^[1]
  1. [1] Mohammed First University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 42, Nº. 1, 2023, págs. 53-63
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5375
• Enlaces
  • Texto completo
• Resumen

  • Let B(X) be the space of all bounded linear operators on complex Banach space X. For A ∈ B(X), we denote by F(A) the subspace of all fixed points of A. In this paper, we study and characterize all surjective maps φ on B(X) satisfying F(φ(T)φ(A) + φ(A)φ(T)) = F(T A + AT) for all A, T ∈ B(X).

     

• Referencias bibliográficas
  • A. Achchi, ”Maps preserving the inner local spectral radius zero of generalized product of operators”, Rendiconti del Circolo Matematico di...
  • Y. Bouramdane, M. Ech-cherif El Kettani, A. Elhiri, and A. lahssaini, “Maps preserving fixed points of generalized product of operators”,...
  • G. Dolinar, S. Du, J. Hou, and P. Legia, ”General preservers of invariant subspace lattices”, Linear algebra and its applications, vol. 429,...
  • M. Elhodaibi and S. Elouazzani, ”Jordan product and inner local spectral radius”, Preprint.
  • A. Guterman, C.-K. Li, and P. Semrl, ”Some general techniques on linear preserver problems”, Linear Algebra and its Applications, vol. 315,...
  • A. A. Jafarian and A. R. Sourour, ”Linear maps that preserve the commutant, double commutant or the lattice of invariant subspaces”, Linear...
  • C. K. Li, P. Semrl and N. S. Sze, ”Maps preserving the nilpotency of products of operators”, Linear algebra and its applications, vol. 424,...
  • C. K. Li, and N. K. Tsing, ”Linear preserver problems: A brief introduction and some special techniques”, Linear algebra and its applications,...
  • 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 V. Darvish, ”Maps preserving the fixed points of triple Jordan products of operators”, Indagationes mathematicae,...