Original scientific paper

https://doi.org/10.21857/y7v64tvgly

Numerical radius points of a bilinear mapping from the plane with the l1-norm into itself,

Sung Guen Kim ; Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea

Abstract

For n ≥ 2 and a Banach space E we let Π(E) = {[x*, x1, . . . , xn] : x*(xj) = ∥x*∥ = ∥xj∥ = 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, . . . , xn] ∈ Π(E) is called a numerical radius point of T ∈ L(nE : E) if |x*(T(x1, . . . , xn))| = 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.

Keywords

Numerical radius; numerical radius attaining bilinear forms; numerical radius points

Hrčak ID:

307492

URI

https://hrcak.srce.hr/307492

Publication date:

25.8.2023.

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