Non Commutative Arens Algebras and their Derivations

2007/03/06 by Sergio Albeverio, Sh. A. Ayupov, Albeverio, S. +3
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.math/0703170

openalex publication_date 2007/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a von Neumann algebra M with a faithful normal semi-finite trace τ, we consider the non commutative Arens algebra L^ω(M, τ)=\bigcap_p≥1L^p(M, τ) and the related algebras L^ω₂(M, τ)=\bigcap_p≥2L^p(M, τ) and M+L^ω₂(M, τ) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M+L^ω₂(M, τ) is inner and all derivations of the algebras L^ω(M,τ) and L^ω₂(M, τ) are spatial and implemented by elements of M+L^ω₂(M, τ).

Related

• Local and 2-Local derivations on noncommutative Arens algebras
• Additive derivations on generalized Arens algebras
• Innerness of Derivations on Subalgebras of Measurable Operators
• Embeddings of ℓ_p into non-commutative spaces
• Structure of derivations on various algebras of measurable operators for type I von Neumann algebras