On maps preserving the Jordan product of $C$-symmetric operators
Given a conjugation $C$ on a complex separable Hilbert space $H$, a bounded linear operator $A$ acting on $H$ is said to be $C$-symmetric if $A=CA^*C$. In this paper, we provide a complete description to all those maps on the algebra of linear operators acting on a finite dimensional Hilbert space that preserve the Jordan product of $C$-symmetric operators, in both directions, for every conjugation $C$ on $H$.
Copyright (c) 2023 Zouheir Amara, Mourad Oudghiri
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