Multiplicatively spectrum-preserving maps on $C^{*}$-algebras

Published 6 Apr 2024 in math.OA and math.FA | (2404.04563v1)

Abstract: We study surjective maps between the sets of all self-adjoint elements of unital $C^*$-algebras which satisfy the multiplicatively spectrum-preserving property. We show that such maps are characterized by Jordan isomorphisms and central symmetries. This is an answer to a problem posed by Moln\'ar.

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