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

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	5537/44183
Uncontrolled Keywords:	Primary 47B47 Secondary 46L51 Derivation local derivation measurable operator τ-compact operator
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	12 Aug 2015 09:07
Last Modified:	23 Oct 2015 17:28
URI:	http://irep.iium.edu.my/id/eprint/44183

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