Computing infima on convex sets, with applications in Hilbert spaces

Authors:
Douglas Bridges, Hajime Ishihara and Luminita Vîta

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2723-2732

MSC (2000):
Primary 03F60, 46S30

Published electronically:
April 8, 2004

MathSciNet review:
2054799

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 and the corresponding operator space This enables us to establish that a bounded, weak-operator totally bounded, convex subset of is strong-operator located.

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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

**Luminita Vîta**

Affiliation:
Department of Mathematics and Statistics, Private Bag 4800, University of Canterbury, Christchurch, New Zealand

Email:
Luminita@math.net

DOI:
https://doi.org/10.1090/S0002-9939-04-07496-9

Keywords:
Functional analysis,
constructive mathematics.

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

Article copyright:
© Copyright 2004
American Mathematical Society