2025/08/29 by Martino Lupini, Lupini, Martino
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Automorphism #Characterization (materials science) #Countable set #Equivalence (formal languages) #Equivalence class (music) #Equivalence relation #Holomorphic and Operator Theory #Separable space #Unital #Unitary state
paper · pdf · doi:10.48550/arxiv.2508.21726
openalex publication_date 2025/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We generalize the notions of Banach space and Fréchet space from the context of topological vector spaces to arbitrary topological groups. We then extend to Banach and Fréchet groups previous results of Saint-Raymond for Banach and Fréchet spaces. We also consider groups with a TSI Polish cover, proving a general comparison criterion for their phantom length. This is applied, together with a dichotomy theorem of Shani, to the study of the derivation length and automorphism length of separable C*-algebras. Building of previous works of Elliott and Akemann--Pedersen, we obtain a general dichotomy theorem for derivations and automorphisms of C*-algebras. We deduce that the derivation length and automorphism length of a separable unital C*-algebras cannot attain certain values, and are in fact (almost) equal to each other for a large class of C*-algebras.