Rad HAZU, Matematičke znanosti, Vol. 27 (2023), 143-151.

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

Sung Guen Kim

Abstract.   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(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. Nradius(T) denotes the set of all numerical radius points of T. In this paper we classify Nradius(T) for every T ∈ L(²l₁² : l₁²) in connection with Norm(T), where Norm(T) denotes the set of all norming points of T.

2020 Mathematics Subject Classification.   46A22.

Key words and phrases.   Numerical radius, numerical radius attaining bilinear forms, numerical radius points.

DOI: https://doi.org/10.21857/y7v64tvgly

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