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

Anwar Mutaqin, Hendra Gunawan

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


Keywords


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

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

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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