Separable Banach spaces which admitl n ∞ approximations

In this paper we study a class of separable Banach spaces which can be approximated by certain special finite-dimensional subspaces. This class is characterized in Theorem 1.1, from which it follows that the space of continuous scalar-valued functions on a compact metric space always belongs to this class, and that every member of this class has a monotone basis. Supported in part by N.S.F. Grant 11-5020. Supported in part by N.S.F. Grant GP-3579.