Let R-N and K-N be the radical ideal and the compact operator ideal of
nest algebra T(N) respectively. It is proved that R-N + K-N = span\ T
is an element of T(N) : TT(N) N subset of or equal to CT\ = span\ T i
s an element of T(N): # sigma'(ST) less than or equal to 1, For All S
is an element of T(N)\.