Open Access

# 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.

### Article Information

 Title Lie derivations on the algebras of locally measurable operators Source Methods Funct. Anal. Topology, Vol. 24 (2018), no. 1, 16-26 MathSciNet MR3783814 Milestones Received 10/05/2017; Revised 05/06/2017 Copyright The Author(s) 2018 (CC BY-SA)

### Authors Information

National University of Uzbekistan, Tashkent, 100174, Uzbekistan

Ilkhom Juraev
Bukhara State University, Bukhara, 100200, Uzbekistan

### 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},
MRNUMBER = {MR3783814},
URL = {http://mfat.imath.kiev.ua/article/?id=1021},
}

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