NUMERICAL RADIUS POINTS OF A BILINEAR MAPPING FROM THE PLANE WITH THE l₁-NORM INTO ITSELF

For n ≥ 2 and a Banach space E we let Π(E) = {[x^∗, x₁, …, x_n]: x^∗ (x_j) = ∥x^∗ ∥ = ∥x_j ∥ = 1 for j = 1, …, n}. Let L(ⁿ E: E) denote the space of all continuous n-linear mappings from E to itself. An element [x^∗, x₁, …, x_n] ∈Π(E) is called a numerical radius point of T ∈ L(ⁿ E: E) if |x^∗ (T (x₁, …, x_n))| = v(T), where v(T) is the numerical radius of T. Nradius(T) denotes the set of all numerical radius points of T. In this paper we classify Nradius(T) for every T ∈ L(² l1^2:l21) in connection with Norm(T), where Norm(T) denotes the set of all norming points of T.