Construction Of Ann-Norm Onℓ p (R)

Abstract

In this article, we discuss ann-norm, withn≥2, which is defined through bounded linear functionals onp-summable sequence spaces. We also introduce a new norm induced by thisn-norm, which will be examined for its equivalence to the usual norm. Next, we demonstrate the relationships between various mappings, including then-norm, (n−1)-norm,· · ·,2-norm, and the usual norm. Finally, our results show that thep-summable sequence spaces, equipped with these mappings are complete spaces.