- Bitlis Eren University Journal of Science and Technology
- Vol: 5 Issue: 1
- $p$-Summable Sequence Spaces with Inner Products
$p$-Summable Sequence Spaces with Inner Products
Authors : Şükran Konca, Mochammad Idris, Hendra Gunawan
Pages : 37-41
Doi:10.17678/beujst.06700
View : 9 | Download : 4
Publication Date : 2015-06-22
Article Type : Other
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 (weighted) inner product space. The relationship between $\ell^p$ and the (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