  The main theorem provides a characterisation of the finite rank operators
lying in a norm closed Lie ideal of a continuous nest algebra. These operators
are charaterised as those finite rank operators in the nest algebra satisfying
a condition determined by a left order continuous homomorphism on the nest. A
crucial fact used in the proof of this theorem is the decomposability of the
finite rank operators. One shows that a finite rank operator in a norm closed
Lie ideal of a continuous nest algebra can be written as a finite sum of rank
one operators lying in the ideal.

Operator Algebras