On the space of p-summable sequences

Authors

  • M. Idris Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia Author
  • S. Ekariani Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia Author
  • H. Gunawan Department of Mathematics, Bandung Institute of Technology, Bandung, Indonesia Author

Keywords:

p-summable sequence space, norm equivalence

Subjects:

46B05, 46B20, 46A45, 46B45

Abstract

On the space p of p-summable sequences(of real numbers), one can derive a norm from the 2-norm asindicated by Gunawan [H. Gunawan, {The space of p-summablesequences and its natural n-norms}, Bull. Austral. Math.Soc. {64} (2001), 137–147]. The purpose of this noteis to establish the equivalence between such a norm andthe usual norm on p. We show that our result is usefulin understanding the topology of p as a 2-normed space.

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Published

2013-01-15