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A theorem on reflexive large rank operator spaces


Author: Lifeng Ding
Journal: Proc. Amer. Math. Soc. 134 (2006), 2881-2884
MSC (2000): Primary 47L05; Secondary 15A04
DOI: https://doi.org/10.1090/S0002-9939-06-08046-4
Published electronically: May 9, 2006
MathSciNet review: 2231611
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Abstract: If every nonzero operator in an $ n$-dimensional operator space $ \mathbb{S}$ has rank $ \geqslant 2n$, then $ \mathbb{S}$ is reflexive.


References [Enhancements On Off] (What's this?)

  • 1. E. A. Azoff, On finite rank operators and preannihilators, Memoirs Amer. Math. Soc. 357 (1986). MR 0858467 (88a:47041)
  • 2. L. Ding, Separating vectors and reflexivity, Lin. Alg. Appl. 174 (1992), 37-52. MR 1176449 (94a:47075)
  • 3. L. Ding, On a pattern of reflexive operator spaces, Proc. Amer. Math. Soc. 124 (1996), 3101-3108. MR 1343689 (97h:47039)
  • 4. D. Hadwin, Algebraically reflexive linear transformations, Lin. Multilin. Alg. 14 (1983), 225-233. MR 0718951 (85e:47003)
  • 5. D. Hadwin, A general view of reflexivity, Trans. Amer. Math. Soc. 344 (1994), 325-360. MR 1239639 (95f:47071)
  • 6. D. R. Larson, Reflexivity, algebraic reflexivity, and linear interpolation, Amer. J. Math. 110 (1988), 283-299. MR 0935008 (89d:47096)
  • 7. J. Li and Z. Pan, Reflexivity and hyperreflexivity of operator spaces, Math. Anal. Appl. 279 (2003), 210-215. MR 1970501 (2004a:47001)
  • 8. H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer-Verlag, 1973. MR 0367682 (51:3924)

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Additional Information

Lifeng Ding
Affiliation: Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303-3083
Email: matlfd@panther.gsu.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08046-4
Keywords: Reflexive operator space, separating vector
Received by editor(s): May 2, 2001
Received by editor(s) in revised form: November 8, 2004
Published electronically: May 9, 2006
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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