Modification of Norms on the Sequence Space ℓp

Salsabilla, Rikha Syahda
Idris, Mochammad

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

In this article, we explore sequence spaces by introducing a newly defined norm. We construct the Orlicz sequence space and demonstrate that the norm in this space is equivalent to the norm in the ℓp space. As a result, the fundamental properties of the ℓp space are carried over to the Orlicz sequence space through the equivalence of norms. One significant implication of this result is that Hölder's inequality, which holds in ℓp spaces, can also be applied to the Orlicz sequence space with different positive constants.