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

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

MathSciNet review:
1328337

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Abstract | References | Similar Articles | Additional Information

Abstract: Let 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 , but must be reflexive if one of these vectors is *strictly* separating. must also be reflexive if all non--zero linear combinations of some independent pair of vectors *strictly* separate .

**1.**E. A. Azoff,*On finite rank operators and preannihilators*, Memoirs Amer. Math. Soc.**357**(1986). MR**88a:47041****2.**E. A. Azoff and H. A. Shehada,*Algebras generated by mutually orthogonal idempotent operators*, J. Operator Theory**29**(1993), 249--267. MR**95h:47063****3.**E. A. Azoff and H. A. Shehada,*Literal embeddings of linear spaces of operators*, Indiana Univ. Math. J.**22**(1993), 571--589. MR**94i:47068****4.**L. Ding,*Separating vectors and reflexivity*, Lin. Alg. Appl.**174**(1992), 37--52. MR**94a:47075****5.**L. Ding,*On strictly separating vectors and reflexivity*, Operator Theory & Integral Equations**19**(1994), 373--380. CMP**94:15****6.**A. Lambert,*Strictly cyclic operator algebras*, Pac. J. Math.**39**(1971), 717--726. MR**46:9762****7.**W.R. Wogen,*Some counterexamples in nonselfadjoint algebras*, Ann. of Math.**126**(1987), 415--427. MR**89b:47066**

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Additional Information

**Edward A. Azoff**

Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403

Email:
azoff@alpha.math.uga.edu

**Lifeng Ding**

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

Email:
matlfd@gsusgi2.gsu.edu

**Warren R. Wogen**

Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599

Email:
wrw@math.unc.edu

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

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