THE NORMING SET OF A SYMMETRIC n-LINEAR FORM ON THE PLANE WITH A ROTATED SUPREMUM NORM FOR n = 3, 4, 5

Let n ∈ N, n ≥ 2. An element (x₁, …, x_n) ∈ Eⁿ is called a norming point of T ∈ L(ⁿE) if ∥x₁∥ = ··· = ∥x_n∥ = 1 and |T(x₁, …, x_n)| = ∥T∥, where L(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ L(ⁿE), we define Norm(T) = n (x₁, …, x_n) ∈ Eⁿ: (x₁, …, x_n) is a norming point of T. Norm(T) is called the norming set of T. Let 0 ≤ θ ≤ (Formula presented.) and (Formula presented.) with the rotated supremum norm ∥(x, y)∥ (∞,θ) = max {|x cos θ + y sin θ|, |x sin θ − y cos θ|}. In this paper, we characterize the norming set of (Formula presented.). Using this result, we completely describe the norming set of (Formula presented.) for n = 3, 4, 5, where (Formula presented.) denotes the space of all continuous symmetric n-linear forms on (Formula presented.). We generalizes the results from [9] for n = 3 and (Formula presented.).