AI

The Maximal Two-Sided Ideals of Nest Algebras

Abstract

We give a necessary and sufficient criterion for an operator in a nest algebra to belong to a proper two-sided ideal of that algebra. Using this result, we describe the strong radical of a nest algebra, and give a general description of the maximal two-sided ideals. This also enables us to provide the final piece in the complete description of epimorphisms of one nest algebra onto another.