$p$-Summable Sequence Spaces with Inner Products

Abstract

We revisit the space $\ell^p$ of $p$-summable sequences of realnumbers. In particular, we show that this space is actuallycontained in a (weighted) inner product space. The relationshipbetween $\ell^p$ and the (weighted) inner product space thatcontains $\ell^p$ is studied. For $p>2$, we also obtain a resultwhich describe how the weighted inner product space is associatedto the weights.