Abstract: We investigate some structure properties of certain valued functions spaces by using new basis definitions of Banach spaces. We show that the space l_∞ has a relative basis and so has an approximation property. Further the linear subspace P(B,X) of l_∞ (B,X) with a precompact rang has an X – Schauder basis. We prove that the Series of C – Schauder basis of l_∞is not unconditional.