Weakly interpolating subspaces

Abstract

A study is made of those n-dimensional subspaces G of C 0(T) which are weakly interpolating. They are more general than the classical Haar or Chebyshev subspaces, or the weak Chebyshev subspaces considered in [2]. Weakly interpolating subspaces G have the property that for each feC0(T) which has a unique best approximation g0 e G, the error f - g0 has at least n+1 peak points. In many cases of interest (e.g. any Chebyshev subspace or the splines), the converse is also valid.