Singly-generated norm closed bimodules of nest algebras

Let NN be a complete nest of a separable Hilbert space HH, algNalgN be the nest algebra with respect to the nest NN, G∈B(H)G∈B(H). We study the norm-principal bimodule of the nest algebra generated by GG. Explicitly, we establish mathematical techniques and construct a type of compact operators with simple structure, which belong to this bimodule, by applying the techniques, which may be related to some classical problems in the theory of nest algebras.