A reduction theory for non-self-adjoint operator algebras
Edward A. Azoff, C. K. Fong, Frank L. Gilfeather · Transactions of the American Mathematical Society · 1976
It is shown that every strongly closed algebra of operators acting on a separable Hilbert space can be expressed as a direct integral of irreducible algebras. In particular, every reductive algebra is the direct integral of transitive algebras. This decomposition is used to study the relationship between the transitive and reductive algebra problems. The final section of the paper shows how to view direct integrals of algebras as measurable algebra-valued functions.