$p$-Summable Sequence Spaces with Inner Products

Year 2015, Volume: 5 Issue: 1, 37 - 41, 22.06.2015

Şükran Konca Mochammad Idris Hendra Gunawan

https://doi.org/10.17678/beujst.06700

Cited By: 2

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

References

• Berberian SK (1961). Introduction to Hilbert Space. Oxford University Press, New York. 1
• Gunawan H, Setya-Budhi W, Mashadi, Gemawati S (2005). On volumes of n -dimensional parallelepipeds on p spaces. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 16, 48-54. 2
• Hilbert D (1912). Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. New York, Chelsea. 3
• Idris M, Ekariani S, Gunawan H (2013). On the space of p - summable sequences. Matematiqki Vesnik, 65 No 1, 58- 63.
• Kreyszig E (1978). Introductory Functional Analysis with Applications. New York, John Wiley & Sons. 5
• Miličić PM (1987). Une généralisation naturelle du produit scaleaire dans un espace normé et son utilisation. Univerzitet u Beogradu. Publ. Inst. Math. (Beograd), 42 No 56, 63-70. 6