Angle in the space of p-summable sequences

The aim of this paper is to investigate completness of A that equipped with usual norm on p-summable sequences space where A is subspace in p-summable sequences space and 1 ≤ p < ∞. We also introduce a new inner product on A and prove completness of A using a new norm that corresponds this new inner product. Moreover, we discuss the angle between two vectors and two subspaces in A. In particular, we discuss the angle between 1-dimensional subspace and (s − 1)-dimensional subspace where s ≥ 2 of A.