Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-06-08632-1
Published electronically: November 29, 2006
MathSciNet review: 2286078
Full-text PDF Free Access

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}$.


References [Enhancements On Off] (What's this?)

  • 1. E. Azoff, On finite rank operators and preannihilators, Memoir Amer. Math. Soc. 357 (1986). MR 0858467 (88a:47041)
  • 2. Lifeng Ding, On a pattern of reflexive operator spaces, Proc. Amer. Math. Soc. (10) 124 (1996), 3101-3108. MR 1343689 (97h:47039)
  • 3. Don Hadwin, A general view of reflexivity, Trans. Amer. Math. Soc. 344 (1994), 325-360. MR 1239639 (95f:47071)
  • 4. Don Hadwin, Algebraically reflexive linear transformations, Linear and Multilinear Algebra (3) 14 (1983), 225-233. MR 0718951 (85e:47003)
  • 5. D. R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), 283-299. MR 0935008 (89d:47096)
  • 6. J. Li and Z. Pan, Reflexivity of finite-dimensional subspaces of operators, J. Oper. Theory. 46 (2001), 381-389. MR 1870413 (2002j:47119)
  • 7. B. Magajna, On the relative reflexivity of finitely generated modules of operators, Trans. Amer. Math. Soc. 327 (1991), 221-249. MR 1038017 (91m:47064)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L05, 15A04

Retrieve articles in all journals with MSC (2000): 47L05, 15A04


Additional Information

Jiankui Li
Affiliation: Department of Mathematics, East China University of Science and Technology, Shanghai 200237, People’s Republic of China
Email: jiankuili@yahoo.com

Zhidong Pan
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, University Center, Michigan 48710
Email: pan@svsu.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08632-1
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

American Mathematical Society