2-Local derivations on von Neumann algebras

Shavkat Ayupov; Karimbergen Kudaybergenov

doi:10.1007/s11117-014-0307-3

2-Local derivations on von Neumann algebras

Shavkat Ayupov
, Karimbergen Kudaybergenov^*

^*Corresponding author for this work

National University of Uzbekistan named after Mirzo Ulugbek
Abdus Salam International Centre for Theoretical Physics
Karakalpak State University

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

The paper is devoted to the description of 2-local derivations on von Neumann algebras. Earlier it was proved that every 2-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of Gleason Theorem for signed measures, we extend this result to type $$III$$III von Neumann algebras. This implies that on arbitrary von Neumann algebra each 2-local derivation is a derivation.

Original language	English
Pages (from-to)	445-455
Number of pages	11
Journal	Positivity
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s11117-014-0307-3
State	Published - 24 Sep 2015
Externally published	Yes

Keywords

2-local derivation
Derivation
von Neumann algebra

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10.1007/s11117-014-0307-3

Cite this

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2-Local derivations on von Neumann algebras

Abstract

Keywords

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