Abstract
If ${\mathscr H}$ is a Hilbert space, $\varphi$ is a (not necessary linear) $*$-surjective mapping on ${\mathbb B}({\mathscr H})$ and $\varphi$ preserves the spectrum of operators of the form $ABA^{*}$, then $\varphi$ is either an algebra automorphism or an algebra anti-automorphism.
Citation
Ali Taghavi Jelodar. Mohammad Sal Moslehian. Abolfazl Sanami. "A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$." Nihonkai Math. J. 21 (1) 1 - 9, 2010.
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