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

Year 2019, , 123 - 129, 20.12.2019

Muh Nur , Hendra Gunawan

https://doi.org/10.33401/fujma.635754

Cited By: 1

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

Supporting Institution

ITB Research and Innovation Program 2019

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