Construction Of An n-Norm On \ell^p (R)

Idris, Mochammad

Journal of the Indonesian Mathematical Society
Vol. 32 No. 2 (2026): JUNE

In this article, we discuss an $n$-norm, with $n \ge 2$, which is defined through bounded linear functionals on $p$-summable sequence spaces. We also introduce a new norm induced by this \( n \)-norm, which will be examined for its equivalence to the usual norm. Next, we demonstrate the relationships between various mappings, including the \( n \)-norm, \( (\!n\!\!-\!\!1\!) \)-norm, $\cdots,$ \( 2 \)-norm, and the usual norm. Finally, our results show that the \( p \)-summable sequence spaces, equipped with these mappings are complete spaces.