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 , acting on a separable Hilbert space, is both commutative and completely distributive, then the algebra generated by the rank-one operators of is dense in 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