An upper bound on the dimension of the reflexivity closure
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- by Calin Ambrozie, Bojan Kuzma and Vladimir Müller PDF
- Proc. Amer. Math. Soc. 138 (2010), 1721-1731 Request permission
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
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1721-1731
- MSC (2010): Primary 47L05; Secondary 15A03
- DOI: https://doi.org/10.1090/S0002-9939-09-10184-3
- MathSciNet review: 2587457