Some remarks on derivations in algebras of measurable operators

2009/07/07 by A. F. Ber, Ber, A. F., B. de Pagter +3
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.0907.1195

14 pages

arxiv created 2009/07/07 · arxiv updated 2009/12/01

Abstract

This paper is concerned with derivations in algebras of (unbounded) operators affiliated with a von Neumann algebra M. Let % A be one of the algebras of measurable operators, locally measurable operators or, τ-measurable operators. We present a complete description of von Neumann algebras M of type I in terms of their central projections such that every derivation in A is inner. It is also shown that every derivation in the algebra LS(M) of all locally measurable operators with respect to a properly infinite von Neumann algebra M vanishes on the center of LS(M).

Related

• 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
• Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra
• Local And 2-Local Derivations On Algebras Of Measurable Operators
• 2-Local derivations on algebras of locally measurable operators