Abstract
It is shown that if the invariant subspace lattice of a reflexive algebra A \mathcal {A} , acting on a separable Hilbert space, is both commutative and completely distributive, then the algebra generated by the rank-one operators of A \mathcal {A} is dense in A \mathcal {A} is any of the strong, weak, ultrastrong or ultraweak topologies. Some related density results are also obtained.
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