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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
For $p>2$, we also obtain a resultwhich describe how the weighted inner product space is associatedto the weights.
📌 3 Key Takeaways
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Objective & Hypothesis:We revisit the space $\ell^p$ of $p$-summable sequences of realnumbers.
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Key Findings & Data:In particular, we show that this space is actuallycontained in a (weighted) inner product space.
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Conclusion & Impact:For $p>2$, we also obtain a resultwhich describe how the weighted inner product space is associatedto the weights.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:inner product spaces · normed spaces · p -summable sequences
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.
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Cite This Article
KONCA, Ş., IDRİS, M., GUNAWAN, H. (2015). $p$-Summable Sequence Spaces with Inner Products. Bitlis Eren University Journal of Science and Technology, Cilt: 5 - Sayı: 1, 37–41. https://ajindex.com/articles/743842