Normalizers of nest algebras

Abstract

For a nest N \mathcal {N} with associated nest algebra A N \mathcal {A}_{\mathcal {N}} , we define S N \mathcal {S}_{\mathcal {N}} , the normalizer of A N \mathcal {A}_{\mathcal {N}} . We develop a characterization of elements of S N \mathcal {S}_{\mathcal {N}} based on certain order homomorphisms of N \mathcal {N} into itself. This characterization enables us to prove several structure theorems.