Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An upper bound on the dimension of the reflexivity closure


Authors: Calin Ambrozie, Bojan Kuzma and Vladimir Müller
Journal: Proc. Amer. Math. Soc. 138 (2010), 1721-1731
MSC (2010): Primary 47L05; Secondary 15A03
Published electronically: November 18, 2009
MathSciNet review: 2587457
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\mathcal V},{\mathcal W}$ be linear spaces over an algebraically closed field, and let $ \mathscr{S}$ be an $ n$-dimensional subspace of linear operators that maps $ {\mathcal V}$ into $ {\mathcal W}$. We give a sharp upper bound for the dimension of the intersection of all images of nonzero operators from $ \mathscr{S}$, namely $ \dim ( \bigcap_{A\in\mathscr{S}\setminus\{0\}}\mathrm{Im} A ) \leq \dim{\mathcal V}-n+1$. As an application, we also give a sharp upper bound for the dimension of the reflexivity closure $ \operatorname{Ref}\mathscr{S}$ of $ \mathscr{S}$, namely $ \dim ( \operatorname{Ref}\mathscr{S} ) \leq n(n+1)/2$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47L05, 15A03

Retrieve articles in all journals with MSC (2010): 47L05, 15A03


Additional Information

Calin Ambrozie
Affiliation: Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1, Czech Republic – and – Mathematical Institute, Bucharest, P.O. Box 1-764, RO-014700 Romania
Email: ambrozie@math.cas.cz

Bojan Kuzma
Affiliation: University of Primorska, Cankarjeva 5, SI-6000 Koper, Slovenia – and – Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia
Email: bojan.kuzma@pef.upr.si

Vladimir Müller
Affiliation: Mathematical Institute of the Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Prague 1, Czech Republic
Email: muller@math.cas.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10184-3
PII: S 0002-9939(09)10184-3
Keywords: Determinantal varieties, space of linear operators, intersection of images, reflexivity defect
Received by editor(s): January 20, 2009
Received by editor(s) in revised form: August 26, 2009
Published electronically: November 18, 2009
Additional Notes: The first author was supported by grants IAA 100190903 of GA AV, Cncsis 54Gr/07, Ancs CEx23-05, MEB 090905
The second author was supported by a joint Czech-Slovene grant, MEB 090905.
The third author was supported by grants No. 201/09/0473 of GA ČR and IRP AV OZ 10190503
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.