Spectral isometries on non-simple C*-algebras

2011/10/31 by Martin Mathieu, Mathieu, Martin, A. R. Sourour +1
Mathematics · #46H10 #46L05 #47A10 #47A65 #47B48 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1110.6856

openalex publication_date 2011/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Related

• A Spectral Characterization of Isomorphisms on C^⋆-Algebras
• A new proof of the noncommutative Banach-Stone theorem
• Non-linear characterization of Jordan *-isomorphisms via maps on positive cones of C^*-algebras
• Multiplicatively spectrum-preserving maps on C^*-algebras
• Invertibility preserving mappings onto finite C*-algebras