Norm-one projections onto subspaces of \((\ell ^{\infty})\) (Q1094631)

Let X be a Banach space and Y a closed subspace of it. A continuous linear operator \(P: X\to Y\) with \(Py=y\) for any y in Y is said a projection onto Y. In approximation theory it is important to characterize those closed subspaces Y for which a norm-one projection exists [see \textit{J. Blatter} and \textit{E. W. Cheney}, Ann. Mat. Pura Appl. IV. Ser. 101, 215-277 (1974; Zbl 0303.46017)]. In this paper we characterize the subspaces of finite codimension in \(\ell ^{\infty}\) which are the range of a norm-one projection. The characterization is given in terms of properties of functions which may describe them.