Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras

Shavkat Ayupov; Karimbergen Kudaybergenov

doi:10.1016/j.jmaa.2013.06.005

Innerness of continuous derivations on algebras of measurable operators affiliated with finite 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

10 Scopus citations

Abstract

This paper is devoted to derivations on the algebra S(M) of all measurable operators affiliated with a finite von Neumann algebra M. We prove that if M is a finite von Neumann algebra with a faithful normal semi-finite trace τ, equipped with the locally measure topology t, then every t-continuous derivation D:S(M)→S(M) is inner. A similar result is valid for derivation on the algebra S(M, τ) of τ-measurable operators equipped with the measure topology t_τ.

Original language	English
Pages (from-to)	256-267
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	408
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2013.06.005
State	Published - 1 Dec 2013
Externally published	Yes

Keywords

Derivation
Inner derivation
Measurable operator

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10.1016/j.jmaa.2013.06.005

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abstract = "This paper is devoted to derivations on the algebra S(M) of all measurable operators affiliated with a finite von Neumann algebra M. We prove that if M is a finite von Neumann algebra with a faithful normal semi-finite trace τ, equipped with the locally measure topology t, then every t-continuous derivation D:S(M)→S(M) is inner. A similar result is valid for derivation on the algebra S(M, τ) of τ-measurable operators equipped with the measure topology tτ.",

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AB - This paper is devoted to derivations on the algebra S(M) of all measurable operators affiliated with a finite von Neumann algebra M. We prove that if M is a finite von Neumann algebra with a faithful normal semi-finite trace τ, equipped with the locally measure topology t, then every t-continuous derivation D:S(M)→S(M) is inner. A similar result is valid for derivation on the algebra S(M, τ) of τ-measurable operators equipped with the measure topology tτ.

KW - Derivation

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KW - Measurable operator

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DO - 10.1016/j.jmaa.2013.06.005

M3 - 文章

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SP - 256

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IS - 1

ER -

Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras

Abstract

Keywords

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