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Proceedings of the American Mathematical Society

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A note on rank-one operators in reflexive algebras


Authors: Cecelia Laurie and W. E. Longstaff
Journal: Proc. Amer. Math. Soc. 89 (1983), 293-297
MSC: Primary 47D25; Secondary 47A15, 47B10
DOI: https://doi.org/10.1090/S0002-9939-1983-0712641-2
MathSciNet review: 712641
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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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DOI: https://doi.org/10.1090/S0002-9939-1983-0712641-2
Article copyright: © Copyright 1983 American Mathematical Society