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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2015
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| Online Access: | http://irep.iium.edu.my/44183/ http://irep.iium.edu.my/44183/1/44183.pdf |
| _version_ | 1848782567910670336 |
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| author | Mukhamedov, Farrukh Kudaybergenov, Karimbergen |
| author_facet | Mukhamedov, Farrukh Kudaybergenov, Karimbergen |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T16:07:31Z |
| format | Article |
| id | iium-44183 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:07:31Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Kudaybergenov, Karimbergen Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras |
| title | 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_short | 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 |
| topic | QA Mathematics |
| 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 |