Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras

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...

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Main Authors:	Mukhamedov, Farrukh, Kudaybergenov, Karimbergen
Format:	Article
Language:	English
Published:	Springer 2015
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/1/44183.pdf

id	iium-44183
recordtype	eprints
spelling	iium-441832015-10-23T09:28:33Z http://irep.iium.edu.my/44183/ Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras Mukhamedov, Farrukh Kudaybergenov, Karimbergen QA Mathematics 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. Springer 2015 Article PeerReviewed application/pdf en http://irep.iium.edu.my/44183/1/44183.pdf Mukhamedov, Farrukh and Kudaybergenov, Karimbergen (2015) Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras. Mediterranean Journal of Mathematics, 12 (3). pp. 1009-1017. ISSN 1660-5454 (O), 1660-5446 (P) http://link.springer.com/journal/9 10.1007/s00009-014-0447-5
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, Farrukh Kudaybergenov, Karimbergen Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
description	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.
format	Article
author	Mukhamedov, Farrukh Kudaybergenov, Karimbergen
author_facet	Mukhamedov, Farrukh Kudaybergenov, Karimbergen
author_sort	Mukhamedov, Farrukh
title	Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
title_short	Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
title_full	Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
title_fullStr	Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
title_full_unstemmed	Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
title_sort	local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras
publisher	Springer
publishDate	2015
url	http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/1/44183.pdf
first_indexed	2023-09-18T21:02:50Z
last_indexed	2023-09-18T21:02:50Z
_version_	1777410738312183808

Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras

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