Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ \(\mathcal{L}\left({}^{n}E\right)\) 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 \(\text{Norm}\left(T\right)=\left\{\left({x}_{1},\dots ,{x}_{n}\right)\in {E}^{n}:\left({x}_{1},\dots ,{x}_{n}\right)\text{ is a norming point of }T\right\}.\)
The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ \(\mathcal{L}\left({}^{m}{l}_{1}^{n}\right)\) , where \({l}_{1}^{n}={\mathbb{R}}^{n}\) with the l1-norm. As applications, we classify Norm(T) for every T ∈ \(\mathcal{L}\left({}^{m}{l}_{1}^{n}\right)\) with n = 2, 3 and m = 2.
