Given a normed space, one can define a new $n$-norm using a semi-inner product $g$ on the space, different from the $n$-norm defined by G\"{a}hler. In this paper, we are interested in the new $n$-norm which is defined using such a functional $g$ on the space $\ell^p$ of $p$-summable sequences, where $1\le p<\infty$. We prove particularly that the new $n$-norm is equivalent with the one defined previously by Gunawan on $\ell^p$.
Equivalence n-norm Semi-inner product g p-summable sequence space
ITB Research and Innovation Program 2019
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 20 Aralık 2019 |
Gönderilme Tarihi | 22 Ekim 2019 |
Kabul Tarihi | 8 Aralık 2019 |
Yayımlandığı Sayı | Yıl 2019 Cilt: 2 Sayı: 2 |