On the problem of continuation of unbounded measures on projectors to weights
The problem of the noncommutative measure theory consisting of studying the possibility of continuing orthoadditive measures on orthoprojectors of von Neumann algebras to linear functionals is considered. The paper contains a construction of a von Neumann algebra \(M\) with no direct terms of type \(I_2\) and a finitely additive unbounded semifinite measure \(m: M^{pr}\to \{0,+\infty\}\), where \(M^{pr}\) is the set of orthoprojectors in \(M^+\), on \(M\) such that \(m\) cannot be extended to a weight.
continuing orthoadditive measures on orthoprojectors of von Neumann algebras to linear functionals
scientific article; zbMATH DE number 1557644