On certain Banach spaces in connection with interpolation theory

By using a norm generated by the error series of a sequence of interpolation polynomials, we obtain in this paper certain Banach spaces. A relation between these spaces and the space (C0,S) with norm generated by the error series of the best polynomial approximations (minimax series) is established. y, certain inequalities for the minimax series of a product are obtained which permit us to define a product over the space (C0,S). With such a product (C0,S) is a Banach Algebra.