This article is cited in 9 papers

Antiproximinal sets in spaces of continuous functions

V. S. Balaganskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spaces $C(Q)$, $C_0(T)$, $L_\infty(S,\Sigma,\mu)$ and $B(S)$, where $Q$ is a topological space and $T$ 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.

UDC: 517.5

Received: 20.02.1995

DOI: 10.4213/mzm1878

 English version: Mathematical Notes, 1996, 60:5, 485–494

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