Multiplicatively spectrum-preserving maps on C^*-algebras

2024/04/06 by Michiya Mori, Mori, Michiya, Shiho Oi +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2404.04563

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 Molnár.

Related

• Non-linear characterization of Jordan *-isomorphisms via maps on positive cones of C^*-algebras
• Spectral isometries on non-simple C*-algebras
• Invertibility preserving mappings onto finite C*-algebras
• Linear maps preserving regularity in C∗-algebras
• Endomorphisms of Stable Continuous-Trace C^*-algebras