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

DOI:
https://doi.org/10.1090/S0002-9939-96-03485-5

MathSciNet review:
1343689

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Abstract | References | Similar Articles | Additional Information

Abstract: A linear subspace is a separating subspace for an operator space if the only member of annihilating is 0. It is proved in this paper that if has a strictly separating vector and a separating subspace satisfying , then is reflexive. Applying this to finite dimensional leads to more results on reflexivity. For example, if dim , and every nonzero operator in has rank , then is reflexive.

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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

DOI:
https://doi.org/10.1090/S0002-9939-96-03485-5

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