Von Neumann introduced the study of rings of operators, through the von Neumann algebras. A von Neumann algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. The von Neumann bicommutant theorem shows that the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. The direct integral was introduced in 1949 by John von Neumann. One of von Neumann's analyses was to reduce the classification of von Neumann algebras on separable Hilbert spaces to the classification of factors. COUNT 4
QSN1 What is von Neumann algebra? ANS1 algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator QSN2 What does the von Neumann bicommutant theorem show? ANS2 the analytic definition is equivalent to a purely algebraic definition as an algebra of symmetries. QSN3 When was direct integral introduced by von Neumann? ANS3 1949 QSN4 What was introduced in von Neumann algebras? ANS4 study of rings of operators