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arXiv · 2210.01654

A note on numerical radius attaining mappings

Mingu Jung
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Abstract

We prove that if every bounded linear operator (or $N$-homogeneous polynomials) with the compact approximation property attains its numerical radius, then $X$ is a finite dimensional space. Moreover, we present an improvement of the polynomial James' theorem for numerical radius proved by Acosta, Becerra Guerrero and Gal$\'a$n in 2003. Finally, the denseness of weakly (uniformly) continuous $2$-homogeneous polynomials on a Banach space whose Aron-Berner extensions attain their numerical radii is obtained.

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Mingu Jung. 2022-10-04. A note on numerical radius attaining mappings. https://arxiv.org/abs/2210.01654

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