Separating versus strictly separating vectors

Azoff, Edward; Ding, Lifeng; Wogen, Warren

doi:10.1090/S0002-9939-96-03381-3

Separating versus strictly separating vectors
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by Edward A. Azoff, Lifeng Ding and Warren R. Wogen

Proc. Amer. Math. Soc. 124 (1996), 3135-3142

DOI: https://doi.org/10.1090/S0002-9939-96-03381-3

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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 $S$.

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