Antiproximinal convex bounded sets in the space \(c_{0}(\gamma )\) equipped with the Day norm

DOI10.1007/s11006-006-0035-5zbMath1122.46004OpenAlexW2008477397MaRDI QIDQ880999

V. S. Balaganskij

Publication date: 21 May 2007

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11006-006-0035-5

zbMATH Keywords

smooth Banach spacesGâteaux differentiabilityweakly compact setsweakly compactly generated Banach spacesrenormingsbest approximation, antiproximinal sets

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (1)

Example of an antiproximinal, but not a 2-antiproximinal convex closed bounded body.

Cites Work

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• Antiproximinal sets in spaces of continuous functions on compacta
• Weakly proximinal sets
• Antiproximal sets
• Some results on nearest points and support properties of convex sets in \(c_ 0\)
• A NOTE ON NEAREST POINTS

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