Local derivations on subalgebras of τ-measurable operators with respect to semi-finite von neumann algebras - Mukhamedov, Farrukh; Kudaybergenov, Karimbergen (Springer, 2015)
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.