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A theorem on reflexive large rank operator spaces
Author(s):
Lifeng
Ding
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2881-2884.
MSC (2000):
Primary 47L05;
Secondary 15A04
Posted:
May 9, 2006
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References |
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Abstract:
If every nonzero operator in an  -dimensional operator space  has rank  , then  is reflexive.
References:
- 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:
10.1090/S0002-9939-06-08046-4
PII:
S 0002-9939(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
Posted:
May 9, 2006
Communicated by:
David R. Larson
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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