Abstract
Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spacesC(Q), C 0(T), L∞(S, S, μ), andB(S), whereQ is a topological space andT is a locally compact Hausdorff space. It is shown that there are no closed bounded antiproximinal sets in Banach spaces with the Radon-Nikodym property.
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Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 643–657, November, 1996.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00196.
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Balaganskii, V.S. Antiproximinal sets in spaces of continuous functions. Math Notes 60, 485–494 (1996). https://doi.org/10.1007/BF02309162
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DOI: https://doi.org/10.1007/BF02309162