Bounded Chebyshev sets in finite-dimensional Banach spaces
Copyright policy )Bounded Chebyshev sets in finite-dimensional Banach spaces
Several necessary and sufficient conditions for all bounded Chebyshev sets in a finite dimensional Banach space to be convex are given. For instance, one such condition is that in the dual sphere the extremal points should form a dense subset. This answers a question raised by Stechkin. The author gives examples, in any dimension \(\geq 3\), of spaces with the property that all bounded Chebyshev sets are convex but there exist unbounded ones which are not convex.
- Lomonosov Moscow State University Russian Federation
Best approximation, Chebyshev systems, bounded Chebyshev sets, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), finite dimensional Banach space
Best approximation, Chebyshev systems, bounded Chebyshev sets, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), finite dimensional Banach space
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