Antiproximinal norms in Banach spaces

DOI10.1006/jath.2001.3636zbMath1037.46012OpenAlexW2054281510WikidataQ56935765 ScholiaQ56935765MaRDI QIDQ1604400

Jonathan M. Borwein, José Pedro Moreno, Mar Jiménez-Sevilla

Publication date: 4 July 2002

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/9c421ea03cf261316447cdf8948afacb54a71ee4

zbMATH Keywords

best approximationRadon-Nikodým propertysupport functionalsantiproximinal sets

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (2)

Relationships Between Farthest Point Problem and Best Approximation Problem ⋮ The \(n\)-antiproximinal sets

Cites Work

• Antiproximinal sets in spaces of continuous functions on compacta
• Differentiability of convex functions and the convex point of continuity property in Banach spaces
• Fréchet differentiable norms on spaces of countable dimension
• Convex antiproximinal sets in spaces \(c_0\) and \(c\)
• Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces
• The relationship between Goldstine's theorem and the convex point of continuity property
• Antiproximinal sets in spaces of continuous functions
• Antiproximal sets
• Geometric aspects of convex sets with the Radon-Nikodym property
• On geometry of Banach spaces with property \(\alpha\)
• Some results on nearest points and support properties of convex sets in \(c_ 0\)
• Counterexamples Concerning Support Theorems for Convex Sets in Hilbert Space
• A Counterexample to a Problem on Points of Continuity in Banach Spaces
• Balls intersection properties of Banach spaces
• A note on norm attaining functionals
• Mazur Intersection Properties and Differentiability of Convex Functions in Banach Spaces
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