Journal of Operator Theory

Volume 95, Issue 1, Winter 2026 pp. 153-158.

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

Authors: Michiya Mori (1), Shiho Oi (2)
Author institution: (1) Faculty of Engineering, Niigata University, Niigata 950-2181, Japan
(2) Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan

Summary: 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 Molnar.

DOI: http://dx.doi.org/10.7900/jot.2024apr06.2460
Keywords: $C^*$-algebras, spectra, Jordan $*$-isomorphisms, preserver problems

Contents Full-Text PDF