THE NORMING SETS OF MULTILINEAR FORMS ON A CERTAIN NORMED SPACE Rⁿ

Let n, m ∈ N, n, m ≥ 2 and E a Banach space. An element (x₁, …, x_n) ∈ Eⁿ is called a norming point of (Formula presented) and (Formula presented), where L(ⁿE) denotes the space of all continuous n-linear forms on E. For (Formula presented), we define Norm(T) as the set of all (x₁, …, x_n) ∈ Eⁿ which are the norming points of T. Let (Formula presented) with a norm satisfying that {W₁, …, W_n} forms a basis and the set of all extreme points of (Formula presented). In the paper we characterize Norm(T) for every (Formula presented) as follows: Let (Formula presented) such that (Formula presented) and A is the Cartesian product of the set {1,…,n}, M is the set of indices (i1,…,im) ∈ A such that (Formula presented).