Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra

2007/03/12 by S. Albeverio, Sh. A. Ayupov, Albeverio, S. +3
Mathematics · #46L50 #46L55 #46L57 #46L60 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L50 #msc:46L55 #msc:46L57 #msc:46L60

paper · pdf · doi:10.48550/arxiv.math/0703331

14 pages

arxiv created 2007/03/12 · arxiv updated 2009/12/01

Abstract

Let M be a type I von Neumann algebra with the center Z, a faithful normal semi-finite trace τ. Let L(M, τ) be the algebra of all τ-measurable operators affiliated with M and let S₀(M, τ) be the subalgebra in L(M, τ) consisting of all operators x such that given any ε>0 there is a projection p\inP(M) with τ(p^⊥)<∞, xp∈ M and ‖xp‖<ε. We prove that any Z-linear derivation of S₀(M, τ) is spatial and generated by an element from L(M, τ).

Related

• Complete description of derivations on τ-compact operators for type I von Neumann algebras
• Structure of derivations on various algebras of measurable operators for type I von Neumann algebras
• Description of Derivations on Measurable Operator Algebras of Type I
• Some remarks on derivations in algebras of measurable operators
• Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra