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Separating versus strictly separating vectors

Authors: Edward A. Azoff, Lifeng Ding and Warren R. Wogen
Journal: Proc. Amer. Math. Soc. 124 (1996), 3135-3142
MSC (1991): Primary 47D15
MathSciNet review: 1328337
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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 [Enhancements On Off] (What's this?)

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Additional Information

Edward A. Azoff
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403

Lifeng Ding
Affiliation: Department of Mathematics and Computer Science, Georgia State University, Atlanta, Georgia 30303-3083

Warren R. Wogen
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599

Keywords: Reflexive operator space, separating vector, strictly separating vector
Received by editor(s): November 28, 1994
Received by editor(s) in revised form: April 3, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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