Bulletin of the Australian Mathematical Society

Research Article

The space of p-summable sequences and its natural n-norm

Hendra Gunawana1

a1 Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia e-mail: hgunawan@dns.math.itb.ac.id

Abstract

We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

(Received November 07 2000)