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Algebraic reflexivity of linear transformations

Authors: Jiankui Li and Zhidong Pan
Journal: Proc. Amer. Math. Soc. 135 (2007), 1695-1699
MSC (2000): Primary 47L05; Secondary 15A04
Published electronically: November 29, 2006
MathSciNet review: 2286078
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal{L}(U, V)$ be the set of all linear transformations from $ U$ to $ V$, where $ U$ and $ V$ are vector spaces over a field $ \mathbb{F}$. We show that every $ n$-dimensional subspace of $ \mathcal{L}(U, V)$ is algebraically $ \lfloor \sqrt {2n} \rfloor $-reflexive, where $ \lfloor t \rfloor $ denotes the largest integer not exceeding $ t$, provided $ n$ is less than the cardinality of $ \mathbb{F}$.

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Additional Information

Jiankui Li
Affiliation: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, People’s Republic of China

Zhidong Pan
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, University Center, Michigan 48710

Keywords: Algebraic reflexivity, separating vector
Received by editor(s): August 21, 2005
Received by editor(s) in revised form: January 5, 2006
Published electronically: November 29, 2006
Additional Notes: This research was partially supported by the NSF of China.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society

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