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 |
| Published: |
Springer
2015
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| Subjects: | |
| 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 |
| Summary: | 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. |
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