Weak*–closed Jordan ideals of nest algebras

Abstract

AbstractNest algebras provide examples of partial Jordan *–triples. If A is a nest algebra and As = A ∩ A*, where A* is the set of the adjoints of the operators lying in A, then (A, As) forms a partial Jordan *–triple. Any weak*–closed ideal in the nest algebra A is also an ideal in the partial Jordan *–triple (A, As). An analysis of the ideal structure of (A, As) shows that, for a large class of nest algebras, the converse is also true.