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Zbl 0861.47022
Azoff, Edward A.; Ding, Lifeng; Wogen, Warren R.
Separating versus strictly separating vectors. (English)
[J] Proc. Am. Math. Soc. 124, No.10, 3135-3142 (1996). ISSN 0002-9939; ISSN 1088-6826/e

Summary: 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 $S$.

MSC 2000:: *47L05 Linear spaces of operators
47L30 Abstract operator algebras on Hilbert spaces

Keywords: strictly separating vectors; linear manifold; Banach space operators; disjoint pair of separating vectors; reflexivity

Cited in: Zbl 1029.47045

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