Unicity subspaces in \(L^ 1\)-approximation (Q1082554)

Let U be an n-dimensional subspace of C[0,1]. U is an \(L^ 1_ w\)- unicity space if to each \(f\in C[0,1]\) there exists a unique best approximant from U to f in the \(L^ 1_ w\)-norm, where w is a positive continuous function and \(\| f\|_ w=\int^{1}_{0}| f(x)| w(x) dx.\) The characterization of unicity spaces is w dependent. This paper totally characterizes all subspaces U which are unicity spaces for all w as above.