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

Published online by Cambridge University Press:  17 April 2009

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

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 137 - 147
Copyright
Copyright © Australian Mathematical Society 2001

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