The Norming Sets of L(2d*(1, w)2)

Abstract

Let 𝑛 ∈ ℕ. An element (x1, … , x𝑛) ∈ En is called a norming point of T ∈ (nE) if ‖x1‖ = ⋯ = ‖xn‖ = 1 and |T (x1, … , xn)| = ‖T‖, where (nE) denotes the space of all continuous n-linear forms on E. For T ∈ (nE), we defineNorm(T) = {(x1, … , xn) ∈ En ∶ (x1, … , xn) is a norming point of T}.Norm(T) is called the norming set of T. We classify Norm(T) for every T ∈ (2𝑑∗(1, w)2), where 𝑑∗(1, w)2 = ℝ2 with the octagonal norm of weight 0 < w < 1 endowed with .