초록
Let n ∈ ℕ, n ≥ 2. An element (x1, . . . , xn) ∈ En is called a norming point of T ∈ 𝓛(nE) if ||x1|| = ··· = ||xn|| = 1 and |T(x1, . . . , xn)| = ||T||, where 𝓛(nE) denotes the space of all continuous n-linear forms on E. For T ∈ 𝓛(nE), we define Norm(T) = {(x1, . . . , xn) ∈ En : (x1, . . . , xn) is a norming point of T}. Norm(T) is called the norming set of T. Let $0{\leq}{\theta}{\leq}{\frac{{\pi}}{4}}$ and ${\ell}^2_{{\infty},{\theta}}={\mathbb{R}}^2$ with the rotated supremum norm $${\parallel}(x,y){\parallel}_{({\infty},{\theta})}={\max}\{{\mid}x\;cos\;{\theta}+y\;sin\;{\theta}{\mid},\;{\mid}x\;sin\;{\theta}-y\;cos\;{\theta}|\}$$. In this paper, we characterize the norming set of T ∈ 𝓛(nℓ2(∞,θ)). Using this result, we completely describe the norming set of T ∈ 𝓛s(nℓ2(∞,θ)) for n = 3, 4, 5, where 𝓛s(nℓ2(∞,θ)) denotes the space of all continuous symmetric n-linear forms on ℓ2(∞,θ). We generalizes the results from [9] for n = 3 and ${\theta}={\frac{{\pi}}{4}}$.