Maximal nilpotent ideals and isomorphisms of large subalgebras of nest algebras

Abstract

Let N be a nest of projections on a Hilbert space H and ℐ (N) be the corresponding nest algebra. Let N be a large subalgebra of ℐ (N). It is proved that any maximal n-nilpotent ideal of A is in the form of A ∩ ℛℱ, where ℱ is a finite subnest of N and ℛℱ is the Jacobson radical of ℐ (ℱ). Using this result can prove that two large subalgebras are isomorphic if and only if the corresponding nests are similar.