EQUIVALENCE OF n-NORMS ON THE SPACE OF p-SUMMABLE SEQUENCES

Anwar Mutaqin; Hendra Gunawan

doi:10.22342/jims.16.1.27.1-7

Anwar Mutaqin ⁽¹⁾, Hendra Gunawan ⁽²⁾

(1) Universitas Sultan Ageng Tirtayasa, Serang, Indonesia,

(2) Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia

https://doi.org/10.22342/jims.16.1.27.1-7

Issue
Volume 16 Number 1 (April 2010)

Submitted
April 28, 2012

Accepted
April 28, 2012

Published
August 5, 2010

Keywords:

n-normed spaces, p-summable sequence spaces, n-norm equivalence

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Abstract

We study the relation between two known n-norms on lp, the space ofp-summable sequences. One n-norm is derived from GÄahler's formula (1969), whilethe other is due to Gunawan (2001). We show in particular that the convergence inone n-norm implies that in the other. The key is to show that the convergence ineach of these n-norms is equivalent to that in the usual norm on lp.

DOI : http://dx.doi.org/10.22342/jims.16.1.27.1-7

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Authors

Anwar Mutaqin

Universitas Sultan Ageng Tirtayasa, Serang

penulis@jims-a.org (Primary Contact)

Hendra Gunawan

Department of Mathematics, Institut Teknologi Bandung, Bandung

Author Biography

Anwar Mutaqin, Universitas Sultan Ageng Tirtayasa, Serang

Department of Mathematics Education

Mutaqin, A., & Gunawan, H. (2010). EQUIVALENCE OF n-NORMS ON THE SPACE OF p-SUMMABLE SEQUENCES. Journal of the Indonesian Mathematical Society, 16(1), 1–7. https://doi.org/10.22342/jims.16.1.27.1-7