Singly-generated norm closed bimodules of nest algebras

Let N be a complete nest of a separable Hilbert space H, algN be the nest algebra with respect to the nest N, G. B(H). We study the norm-principal bimodule of the nest algebra generated by G. 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. (C) 2011 Elsevier Ltd. All rights reserved.