EQUIVALENCE OF n-NORMS ON THE SPACE OF p-SUMMABLE SEQUENCES - Anwar Mutaqin; Hendra Gunawan (Journal of the Indonesian Mathematical Society, 2010)
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