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Approximation properties of sets with bounded complements

Published online by Cambridge University Press:  14 November 2011

C. Franchetti  and
P. L. Papini
C. Franchetti
Affiliation:
University of Genova, Italy
P. L. Papini
Affiliation:
University of Bologna, Italy
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Synopsis

Given a Banach space X, we investigate the behaviour of the metric projection PF onto a subset F with a bounded complement.

We highlight the special role of points at which d(x, F) attains a maximum. In particular, we consider the case of X as a Hilbert space: this case is related to the famous problem of the convexity of Chebyshev sets.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 1-2 , 1981 , pp. 75 - 86
Copyright
Copyright © Royal Society of Edinburgh 1981

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