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},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a1/}
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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/