Nest algebra

Summary

A nest is a totally ordered and complete family of closed subspaces of a Hilbert space. The nest algebra of a nest is the algebra of all bounded operators that leave every subspace of the nest invariant. Nest algebras are the infinite-dimensional analogues of the algebras of upper triangular matrices. They are the main examples of non-self-adjoint operator algebras, and every nest algebra is a reflexive operator algebra.