Local Derivations on Subalgebras of τ-Measurable Operators with Respect to Semi-finite von Neumann Algebras

Farrukh Mukhamedov, Karimbergen Kudaybergenov

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Abstract

This paper is devoted to local derivations on subalgebras on the algebra S(M, τ) of all τ-measurable operators affiliated with a von Neumann algebra M without abelian summands and with a faithful normal semi-finite trace τ. We prove that if A is a solid *-subalgebra in S(M, τ) such that p∈A for all projection p ∈ M with finite trace, then every local derivation on the algebra A is a derivation. This result is new even in the case of standard subalgebras on the algebra B(H) of all bounded linear operators on a Hilbert space H. We also apply our main theorem to the algebra S0(M, τ) of all τ-compact operators affiliated with a semi-finite von Neumann algebra M and with a faithful normal semi-finite trace τ.

Original languageEnglish
Pages (from-to)1009-1017
Number of pages9
JournalMediterranean Journal of Mathematics
Volume12
Issue number3
DOIs
Publication statusPublished - Jul 8 2015
Externally publishedYes

Keywords

  • Derivation
  • local derivation
  • measurable operator
  • τ-compact operator

ASJC Scopus subject areas

  • General Mathematics

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