A note on numerical radius attaining mappings

Jung, Mingu

doi:10.1090/proc/16457

A note on numerical radius attaining mappings
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by Mingu Jung;

Proc. Amer. Math. Soc. 151 (2023), 4419-4434

DOI: https://doi.org/10.1090/proc/16457

Published electronically: May 12, 2023

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Abstract:

We prove that if every bounded linear operator (or $N$-homogeneous polynomials) on a Banach space $X$ 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 Galán [Q. J. Math. 54 (2003), pp. 1–10]. 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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A note on numerical radius attaining mappings
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