Numerical radius peak multilinear mappings on ℓ₁

For n ≥ 2 and a Banach space E, L(ⁿ E: E) denotes the space of all continuous n-linear mappings from E to itself. We let (Formula presented). An element [x^∗, x₁, …, x_n ] ∈ Π(E) is called a numerical radius point of (Formula presented), where the numerical radius (Formula presented), we define (Formula presented) is a numerical radius point of T}. Nradius(T) is called the set of all numerical radius points for T. T is called numerical radius peak n-linear mapping if (Formula presented). In this paper we investigate Nradius(T) for every T ∈ L(ⁿ ℓ₁: ℓ₁) and characterize all numerical radius peak multilinear mappings in L(ⁿ ℓ₁: ℓ₁), where ℓ₁ is a real or complex space.