Geodesic
Maps Preserving the Spectrum of Skew Lie Product of Operators
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 525 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $\lh$ denote the algebra of all bounded linear operators acting on a complex Hilbert space $\h$. In this paper, we show that a surjective map $\vf$ on $\lh$ satisfies \[ igmaeft(ǎrphi(T)ǎrphi(S)-ǎrphi(S)ǎrphi(T)^*\right)=igmaeft(TS-ST^*\right),\quad T,Sıh, \] if and only if there exists a unitary operator $U\in \lh$ such that \[ǎrphi(T)=ambda UTU^{*}, \quad Tıh,\] where $\lambda\in\left\{-1, 1\right\}$.
Classification : 47B49 47A10, 47A11
Keywords: Nonlinear preservers, spectrum, Skew Lie product 
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     author = {Eman Alzedani and Mohamed Mabrouk},
     title = {Maps {Preserving} the {Spectrum} of {Skew} {Lie} {Product} of {Operators}},
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     year = {2022},
     language = {en},
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Eman Alzedani; Mohamed Mabrouk. Maps Preserving the Spectrum of Skew Lie Product of Operators. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 525 . http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a1/