New 2-norms formed on ℓp(ℝ) by bounded linear functionalsS. Konca, M. IdrisThe space of p-summable sequences of real numbers ℓp(ℝ), can be equipped with norm or n-norm with n≥2. In this work, we consider two new 2-norms formed on ℓp(ℝ) based on different choices of bounded linear functionals on it and investigate their relationships between Gähler's and Gunawan's 2-norms. One of these 2-norms is a special case of the 2-norm defined very recently by Konca and Idris [A new 2-norm generated by bounded linear functionals on a normed space, Filomat, 2023.]. They have wondered whether 2-norm defined by them and Gähler's 2-norm are strongly equivalent or not for some special cases of a normed space X. A part of this work consists the solution of the open problem given by them for X=ℓp(ℝ). We define new two 2-norms and show that those are not always equivalent to the usual 2-norm on ℓp(ℝ). One of the newly defined norms induced from these new 2-norms, is equivalent to the usual norm on ℓp(ℝ), while the other one is not. These differences are obtained as a result of depending on the chosen bounded linear functionals to form new 2-norms and norms on this space.Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16, supplement issue 4 (2023), pp. 151-165 |