On the space of p-summable sequences
Idris M.a, Ekariani S.b, Gunawan H.b
a Department of Mathematics, Universitas Lambung Mangkurat, Indonesia
b Department of Mathematics, Bandung Institute of Technology, Indonesia
Abstract
On the space l p of p-summable sequences (of real numbers), one can derive a norm from the 2-norm as indicated by Gunawan [H. Gunawan, The space of p-summable sequences and its natural n-norms, Bull. Austral. Math. Soc. 64 (2001), 137-147]. The purpose of this note is to establish the equivalence between such a norm and the usual norm on l p. We show that our result is useful in understanding the topology of l p as a 2-normed space.
Author keywords
Indexed keywords
Norm equivalence,P-summable sequence spaces