Reflexive operator algebra

Summary

A reflexive operator algebra is an algebra of operators on a Hilbert space that is determined by its invariant subspaces. It contains every operator that leaves all of them invariant. Reflexivity links the algebraic structure of operator algebras with the lattice of their invariant subspaces. Von Neumann algebras and nest algebras are reflexive, and the question of which algebras are reflexive is close to the invariant subspace problem.