2009/08/09 by Shavkat Ayupov, Ayupov, Shavkat A., Karimbergen Kudaybergenov +1 · 5 citations
Mathematics · #46L50 #46L55 #46L57 #46L60 #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.0908.1202
openalex publication_date 2009/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a von Neumann algebra M we introduce so called central extension mix(M) of M. We show that mix(M) is a *-subalgebra in the algebra LS(M) of all locally measurable operators with respect to M, and this algebra coincides with LS(M) if and only if M does not admit type II direct summands. We prove that if M is a properly infinite von Neumann algebra then every additive derivation on the algebra mix(M) is inner. This implies that on the algebra LS(M), where M is a type I_∞ or a type III von Neumann algebra, all additive derivations are inner derivations.