THE NUMERICAL RADIUS POINTS OF L(² ℓ²_(∞,θ): ℓ²_(∞,θ))

For n ≥ 2 and a Banach space E we let (Formula presented.) L (ⁿE : 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(ⁿE : E) if |x* (T(x₁,..., x_n))| = v(T), where v(T) is the numerical radius of T. By Nradius(T) we denote the set of all numerical radius points of T. Let (Formula presented.) and (Formula presented.) with the rotated supremum norm (Formula presented.). In this paper, we show that the numerical radius of T ∈ L(² ℓ²_(∞,θ): ℓ²_(∞,θ)) equals to its norm ||T||. Using this, we classify Nradius(T) for every T ∈ L(² ℓ²_(∞,θ): ℓ²_(∞,θ)) in connection with the norming points of the bilinear mapping associated with T. Let (Formula presented.) and (Formula presented.) We also show that (Formula presented.), which generalizes some results in [12].