Vector valued chebechev systems

Abstract

Let I be the unit interval and X be a real Banach space. The space of continuous functions on I with values in X is denoted by C(I,X). The object of this paper is to introduce Chebechev systems in C(I,X) and study the basi.c properties of such systems, and its relation to interpolation. It is also proved that a subspace that is generated by a weak Chebechev system in C(I,X) is a Chebechev subspace.