Three Equivalent n-Norms on the Space of p-Summable Sequences

Authors : Muh NUR, Hendra GUNAWAN

Pages : 123-129

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Publication Date : 2019-12-20

Article Type : Research Paper

Abstract :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 $\ell^p$.
Keywords : Equivalence, n norm, Semi inner product g, p summable sequence space