Weak-local derivations and homomorphisms on C*-algebras

2014/11/18 by Ahlem Ben Ali Essaleh, Essaleh, Ahlem Ben Ali, Antonio M. Peralta +3
Materials Science · Mathematics · #46L57 #47B44 #47B48 #47B49 #47L10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Organic and Molecular Conductors Research #Primary 47B47 #Secondary 15A86

paper · pdf · doi:10.48550/arxiv.1411.4795

openalex publication_date 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every weak-local derivation on a C^*-algebra is continuous, and the same conclusion remains valid for weak^*-local derivations on von Neumann algebras. We further show that weak-local derivations on C^*-algebras and weak^*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal ^*-automorphism with our notions of extreme-strong-local derivations and automorphisms.

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