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.
Original language | English |
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Pages (from-to) | 1009-1017 |
Number of pages | 9 |
Journal | Mediterranean Journal of Mathematics |
Volume | 12 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jul 8 2015 |
Externally published | Yes |
Keywords
- Derivation
- local derivation
- measurable operator
- τ-compact operator
ASJC Scopus subject areas
- Mathematics(all)