The n-Normed Space of p-Summable sequences

Abstract

This dissertation deals with the detail of a paper of H. Gunawan that studies the space ` p, 1 ≤ p ≤ ∞ and its natural n-norm, which can be viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, by showing that ` p is complete with respect to its natural n-norm and the n-dual of ` p under two important n-norms. In addition, it also gives a weak p-summable space of an ` p sequences as an n-normed space.