Minimal rank and reflexivity of operator spaces

Authors:
Roy Meshulam and Peter Semrl

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1839-1842

MSC (2000):
Primary 47L05; Secondary 15A03

Published electronically:
December 29, 2006

MathSciNet review:
2286094

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an -dimensional space of linear operators between the linear spaces and over an algebraically closed field . Improving results of Larson, Ding, and Li and Pan we show the following.

**Theorem.**

*Let be a basis of . Assume that every nonzero operator in has rank larger than . Then a linear operator belongs to if and only if for every , is a linear combination of*.

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Additional Information

**Roy Meshulam**

Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel

Email:
meshulam@math.technion.ac.il

**Peter Semrl**

Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Email:
peter.semrl@fmf.uni-lj.si

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08671-0

Received by editor(s):
April 7, 2005

Received by editor(s) in revised form:
February 10, 2006

Published electronically:
December 29, 2006

Additional Notes:
The research of the first author was supported in part by the Israel Science Foundation

The research of the second author was supported in part by a grant from the Ministry of Science of Slovenia

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.