The geometric rank and isometries of radical-type ideals in nest algebras

Let T (N) be a nest algebra. A left (right) ideal J of T (N) is said to be radical-type if a compact operator K belongs to J if and only if K belongs to the Jacobson radical of T (N). In this paper, the geometric rank of finite rank operators in radical-type left ideals and isometries of these ideals are studied. Let J be a radical-type left ideal of T (N). It is shown that any finite rank operator in J has finite geometric rank if and only if the condition is satisfied: if N ∈ N with 0+