A note on numerical radius attaining mappings

Author:

Jung Mingu

Abstract

We prove that if every bounded linear operator (or N N -homogeneous polynomials) on a Banach space X X with the compact approximation property attains its numerical radius, then X 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 2 -homogeneous polynomials on a Banach space whose Aron-Berner extensions attain their numerical radii is obtained.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference41 articles.

1. Some results on operators that attain their numerical radius;Acosta, Maria D.,1991

2. Numerical-radius-attaining polynomials;Acosta, M. D.;Q. J. Math.,2003

3. James type results for polynomials and symmetric multilinear forms;Acosta, Maria D.;Ark. Mat.,2004

4. A version of James’ theorem for numerical radius;Acosta, María D.;Bull. London Math. Soc.,1999

5. Denseness of operators whose second adjoints attain their numerical radii;Acosta, María D.;Proc. Amer. Math. Soc.,1989

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