Geodesic
Operators of Rank One in Reflexive Algebras
Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 19-23

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If H is a (complex) Hilbert space and is a collection of (closed linear) subspaces of H it is easily shown that the set of all (bounded linear) operators acting on H which leave every member of invariant is a weakly closed operator algebra containing the identity operator. This algebra is denoted by Alg . In the study of such algebras it may be supposed [4] that is a subspace lattice i.e. that is closed under the formation of arbitrary intersections and arbitrary (closed linear) spans and contains both the zero subspace (0) and H. The class of such algebras is precisely the class of reflexive algebras [3]. 
Longstaff, W. E. Operators of Rank One in Reflexive Algebras. Canadian journal of mathematics, Tome 28 (1976) no. 1, pp. 19-23. doi: 10.4153/CJM-1976-003-1
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