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.

**1.**B. Aupetit,*An improvement of Kaplansky's lemma on locally algebraic operators*, Studia Math.**88**(1988), 275-278. MR**89d:47002****2.**E. A. Azoff,*On finite rank operators and preannihilators*, Memoirs Amer. Math. Soc.**357**(1986). MR**88a:47041****3.**E. A. Azoff, L. Ding and W. R. Wogen,*Separating versus strictly separating vectors*, to appear in Proc. Amer. Math. Soc.. CMP**95:11****4.**L. Ding,*Separating vectors and reflexivity*, Lin. Alg. Appl.**174**(1992), 37-52. MR**94a:47075****5.**L. Ding,*On strictly separating vectors and reflexivity*, Integ. Equat. Oper. Th.**19**(1994), 373-380. CMP**94:15****6.**W. Gong, D. R. Larson and W. R. Wogen,*Two results on separating vectors*, preprint.**7.**D. Hadwin,*Algebraically reflexive linear transformations*, Lin. Multilin. Alg.**14**(1983), 225-233. MR**85e:47003****8.**D. Hadwin,*A general view of reflexivity*, Trans. Amer. Math. Soc.**344**(1994), 325-360. MR**95f:47071****9.**D. Hadwin and E.A. Nordgren,*Reflexivity and direct sums*, Acta Sci. Math.(Szeged)**55**(1991), 181-197. MR**92g:47064****10.**P. R. Halmos,*A Hilbert space problem book*, 2nd ed., Springer-Verlag, New York, 1982. MR**84e:47001****11.**D. R. Larson,*Reflexivity, algebraic reflexivity, and linear interpolation*, Amer. J. Math.**110**(1988), 283- 299. MR**89d:47096****12.**L. Livshits,*Locally finite-dimensional sets of operators*, Proc. Amer. Math. Soc.**119**(1993), 165-169. MR**93k:47054****13.**B. Magajna,*On the relative reflexivity of finitely generated modules of operators*, Trans. Amer. Math. Soc.**327**(1991), 221-249. MR**91m:47064**

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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