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

S. Albeverio; Sh. A. Ayupov; K. K. Kudaybergenov

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

Operator Algebras 2008-08-07 v2 Functional Analysis

Authors: S. Albeverio , Sh. A. Ayupov , K. K. Kudaybergenov

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 $LS(M).$

Keywords

von neumann algebra measurable operators derivations type i inner derivation

Cite

@article{arxiv.math/0703171,
  title  = {Derivations on the Algebra of Measurable Operators Affiliated with a Type I von Neumann Algebra},
  author = {S. Albeverio and Sh. A. Ayupov and K. K. Kudaybergenov},
  journal= {arXiv preprint arXiv:math/0703171},
  year   = {2008}
}

Comments

12 pages

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