On a pattern of reflexive operator spaces
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Abstract:
A linear subspace $M$ is a separating subspace for an operator space $S$ if the only member of $S$ annihilating $M$ is 0. It is proved in this paper that if $S$ has a strictly separating vector $x$ and a separating subspace $M$ satisfying $Sx \cap [SM] = \{0\}$, then $S$ is reflexive. Applying this to finite dimensional $S$ leads to more results on reflexivity. For example, if dim $S = n$, and every nonzero operator in $S$ has rank $> n^{2}$, then $S$ is reflexive.References
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Additional Information
- Lifeng Ding
- Affiliation: Department of Mathematics & Computer Science, Georgia State University, Atlanta, Georgia 30303-3083
- Email: matlfd@gsusgi2.gsu.edu
- Received by editor(s): October 14, 1994
- Received by editor(s) in revised form: March 30, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3101-3108
- MSC (1991): Primary 47D15; Secondary 15A30
- DOI: https://doi.org/10.1090/S0002-9939-96-03485-5
- MathSciNet review: 1343689