Computing infima on convex sets, with applications in Hilbert spaces
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- by Douglas Bridges, Hajime Ishihara and Luminiţa Vîţă PDF
- Proc. Amer. Math. Soc. 132 (2004), 2723-2732 Request permission
Abstract:
Using intuitionistic logic, we prove that under certain reasonable conditions, the infimum of a real-valued convex function on a convex set exists. This result is then applied to problems of simultaneous approximation in Hilbert space $H$ and the corresponding operator space $\mathcal {B}\left (H\right ).$ This enables us to establish that a bounded, weak-operator totally bounded, convex subset of $\mathcal {B}\left ( H\right )$ is strong-operator located.References
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Additional Information
- Douglas Bridges
- Affiliation: Department of Mathematics and Statistics, Private Bag 4800, University of Canterbury, Christchurch, New Zealand
- Email: d.bridges@math.canterbury.ac.nz
- Hajime Ishihara
- Affiliation: School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan
- Email: ishihara@jaist.ac.jp
- Luminiţa Vîţă
- Affiliation: Department of Mathematics and Statistics, Private Bag 4800, University of Canterbury, Christchurch, New Zealand
- Email: Luminita@math.net
- Received by editor(s): January 6, 2003
- Published electronically: April 8, 2004
- Additional Notes: Bridges and Vîţă gratefully acknowledge the support of the Marsden Fund and FoRST New Zealand. All three authors thank the Japan Advanced Institute of Science & Technology for supporting the visit by the first two during which much of this work was carried out.
- Communicated by: Jonathan M. Borwein
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2723-2732
- MSC (2000): Primary 03F60, 46S30
- DOI: https://doi.org/10.1090/S0002-9939-04-07496-9
- MathSciNet review: 2054799