Jordan product and fixed points preservers
DOI:
https://doi.org/10.22199/issn.0717-6279-5375Keywords:
fixed points, Jordan product, preserverAbstract
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).
References
A. Achchi, ”Maps preserving the inner local spectral radius zero of generalized product of operators”, Rendiconti del Circolo Matematico di Palermo Series 2, vol. 68, no. 2, pp. 355-362, 2018. https://doi.org/10.1007/s12215-018-0363-9
Y. Bouramdane, M. Ech-cherif El Kettani, A. Elhiri, and A. lahssaini, “Maps preserving fixed points of generalized product of operators”, Proyecciones (Antofagasta), vol. 39, no 5, pp. 1157-1165, 2020. https://doi.org/10.22199/issn.0717-6279-2020-05-0071
G. Dolinar, S. Du, J. Hou, and P. Legia, ”General preservers of invariant subspace lattices”, Linear algebra and its applications, vol. 429, no 1, pp. 100-109, 2008. https://doi.org/10.1016/j.laa.2008.02.007
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, no 1-3, pp. 61-81, 2000. https://doi.org/10.1016/s0024-3795(00)00119-1
A. A. Jafarian and A. R. Sourour, ”Linear maps that preserve the commutant, double commutant or the lattice of invariant subspaces”, Linear and multilinear algebra, vol. 38, no. 1-2, pp. 117-129, 1994. https://doi.org/10.1080/03081089508818345
C. K. Li, P. Semrl and N. S. Sze, ”Maps preserving the nilpotency of products of operators”, Linear algebra and its applications, vol. 424, no 1, pp. 222-239, 2007. https://doi.org/10.1016/j.laa.2006.11.013
C. K. Li, and N. K. Tsing, ”Linear preserver problems: A brief introduction and some special techniques”, Linear algebra and its applications, vol. 162, pp. 217-235, 1992. https://doi.org/10.1016/0024-3795(92)90377-m
A. Taghavi and R. Hosseinzadeh, ”Maps preserving the dimension of fixed points of products of operators”, Linear and multilinear algebra, vol. 62, no. 10, pp. 1285-1292, 2013. https://doi.org/10.1080/03081087.2013.823680
A. Taghavi, R. Hosseinzadeh, and V. Darvish, ”Maps preserving the fixed points of triple Jordan products of operators”, Indagationes mathematicae, vol. 27, no. 3, pp. 850-854, 2016. https://doi.org/10.1016/j.indag.2016.03.003
Published
How to Cite
Issue
Section
Copyright (c) 2023 Mhamed Elhodaibi, Soufiane Elouazzani
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.