This article is cited in 8 papers

The conditional Chebyshev center of a compact set of continuous functions

A. L. Garkavi


Abstract: We establish characteristic properties of a subspace $L$ of finite codimension of the space $C(T)$ that has a Chebyshev center and a Chebyshev net for every compact set from $C(T)$. We show that these properties are the same as the conditions for the existence in $L$ of an element of best approximation for every element from $C(T)$.

UDC: 517.5

Received: 16.10.1972

 English version: Mathematical Notes, 1973, 14:4, 827–831

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