$p$-Summable Sequence Spaces with Inner Products

Authors : Şükran KONCA, Mochammad IDRİS, Hendra GUNAWAN

Pages : 37-41

Doi:10.17678/beujst.06700

View : 15 | Download : 9

Publication Date : 2015-06-22

Article Type : Research Paper

Abstract :We revisit the space $\ell^p$ of $p$-summable sequences of real numbers. In particular, we show that this space is actually contained in a insert ignore into journalissuearticles values(weighted); inner product space. The relationship between $\ell^p$ and the insert ignore into journalissuearticles values(weighted); inner product space that contains $\ell^p$ is studied. For $p>2$, we also obtain a result which describe how the weighted inner product space is associated to the weights.
Keywords : inner product spaces, normed spaces, p summable sequences, weights