Complete description of derivations on τ-compact operators for type I von Neumann algebras

2008/07/27 by S. Albeverio, Sh. A. Ayupov, Albeverio, S. +7
Mathematics · #46L50 #46L55 #46L57 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L50 #msc:46L55 #msc:46L57

paper · pdf · doi:10.48550/arxiv.0807.4316

19 pages

arxiv created 2008/07/27 · openalex publication_date 2008/07/27 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Given a type I von Neumann algebra M with a faithful normal semi-finite trace τ, let S₀(M, τ) be the algebra of all τ-compact operators affiliated with M. We give a complete description of all derivations on the algebra S₀(M, τ). In particular, we prove that if M is of type I_∞ then every derivation on S₀(M, τ) is spatial.

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• Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra
• Description of Derivations on Measurable Operator Algebras of Type I
• Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra
• Some remarks on derivations in algebras of measurable operators