Local derivations of nest subalgebras of von Neumann algebras
Let \(\delta\colon A\rightarrow M\) be a linear map from an algebra \(A\) into an \(A\)-bimodule \(M\). The map \(\delta\) is said to be a local derivation if for each \(a\in A\) there exists a derivation \(\delta_a: A\rightarrow M\) such that \(\delta(a)=\delta_a(a)\). It is said to be a 2-local derivation if for all \(a,b\in A\) there exists a derivation \(\delta_{a,b}\colon A\rightarrow M\) such that \(\delta(a)=\delta_{a,b}(a)\) and \(\delta(b)=\delta_{a,b}(b)\). In the paper under review, it is shown that if \(M\) is a factor von Neumann algebra and \(A\) is a nest subalgebra of \(M\), then any continuous local derivation and any 2-local derivation from \(A\) into \(M\) are necessarily derivations.
scientific article; zbMATH DE number 2119128
scientific article