A note on rank-one operators in reflexive algebras

Laurie, Cecelia; Longstaff, W. E.

doi:10.1090/S0002-9939-1983-0712641-2

A note on rank-one operators in reflexive algebras
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by Cecelia Laurie and W. E. Longstaff PDF

Proc. Amer. Math. Soc. 89 (1983), 293-297 Request permission

Abstract:

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

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