Recent progress and open questions on the numerical index of Banach spaces

Abstract

The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.

27 pages, 4 figures, to appear in RACSAM

References in corpus (2)

• Numerical index and duality
• An elementary approach to the Daugavet equation

Cited by in corpus (10)

• The group of isometries of a Banach space and duality
• Lipschitz slices and the Daugavet equation for Lipschitz operators
• On the Bishop-Phelps-Bollobás property for numerical radius
• Two-dimensional Banach spaces with Polynomial numerical index zero
• On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space
• L- and M-structure in lush spaces
• Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices
• A sharp inequality involving hyperbolic and inverse hyperbolic functions
• On the Bishop-Phelps-Bollobas property for numerical radius in C(K)-spaces
• The Bishop-Phelps-Bollobás property for numerical radius in ${\ell }_1(\mathbb{C})$