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Separating versus strictly separating vectors

Author(s): Edward A. Azoff; Lifeng Ding; Warren R. Wogen
Journal: Proc. Amer. Math. Soc. 124 (1996), 3135-3142.
MSC (1991): Primary 47D15
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Abstract: Let $S$ be a linear manifold of Banach space operators which is closed in the strong operator topology. Existence of a disjoint pair of separating vectors does not guarantee reflexivity of $S$ , but $S$ must be reflexive if one of these vectors is strictly separating. $S$ must also be reflexive if all non--zero linear combinations of some independent pair of vectors strictly separate $S$ .

References:

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7.: W.R. Wogen, Some counterexamples in nonselfadjoint algebras, Ann. of Math. 126 (1987), 415--427. MR 89b:47066


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