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Proceedings of the American Mathematical Society

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On a pattern of reflexive operator spaces

Author: Lifeng Ding
Journal: Proc. Amer. Math. Soc. 124 (1996), 3101-3108
MSC (1991): Primary 47D15; Secondary 15A30
MathSciNet review: 1343689
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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.

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

Keywords: Reflexive operator space, separating vector, separating space
Received by editor(s): October 14, 1994
Received by editor(s) in revised form: March 30, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society