Abstract
Let N be a complete nest in a separable Hilbert space H , and let alg N be the nest algebra related to N . We obtain necessary and sufficient conditions for, B( H ) to be principally generated as a norm-closed bimodule of alg N . The same conditions characterize when B( H ) is principally generated as a norm-closed bimodule of the quasitriangular algebra alg N + K , and when the Calkin algebra is principally generated as a norm-closed bimodule of the image of alg N under the Calkin homomorphism. In each case countable generation is equivalent to principal generation.
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