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Lie derivations on the algebras of locally measurable operators


Abstract

We prove that every Lie derivation on a solid $\ast$-subalgebra in an algebra of locally measurable operators is equal to a sum of an associative derivation and a center-valued trace.

Key words: Von Neumann algebras, locally measurable operator, derivation, Lie derivation, center-valued trace.


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Article Information

TitleLie derivations on the algebras of locally measurable operators
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 16-26
MilestonesReceived 10/05/2017; Revised 05/06/2017
CopyrightThe Author(s) 2018 (CC BY-SA)

Authors Information

Vladimir Chilin
National University of Uzbekistan, Tashkent, 100174, Uzbekistan 

Ilkhom Juraev
Bukhara State University, Bukhara, 100200, Uzbekistan 


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Citation Example

Vladimir Chilin and Ilkhom Juraev, Lie derivations on the algebras of locally measurable operators, Methods Funct. Anal. Topology 24 (2018), no. 1, 16-26.


BibTex

@article {MFAT1021,
    AUTHOR = {Vladimir Chilin and Ilkhom Juraev},
     TITLE = {Lie derivations on the algebras of locally measurable  operators},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {16-26},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1021},
}


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