Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra

2007/03/06 by S. Albeverio, Sergio Albeverio, Sh. A. Ayupov +5
Mathematics · #46L50 #46L55. 46L60 #46L57 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L50 #msc:46L55. #msc:46L57 #msc:46L60

paper · pdf · doi:10.48550/arxiv.math/0703171

12 pages

openalex publication_date 2007/03/06 · arxiv created 2008/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a type I von Neumann algebra with the center Z, and let LS(M) be the algebra of all locally measurable operators affiliated with M. We prove that every Z-linear derivation on LS(M) is inner. In particular all Z-linear derivations on the algebras of measurable and respectively totally measurable operators are spatial and implemented by elements from LS(M).

Related

• Structure of derivations on various algebras of measurable operators for type I von Neumann algebras
• Some remarks on derivations in algebras of measurable operators
• Description of Derivations on Measurable Operator Algebras of Type I
• Additive derivations on algebras of measurable operators
• 2-Local derivations on algebras of locally measurable operators