Reflexivity and non-weakly null maximizing sequences

Abstract

We introduce and explore a new property related to reflexivity that plays an important role in the characterization of norm attaining operators. We also present an application to the theory of compact perturbations of linear operators and characterize norm attaining scalar-valued continuous $2$-homogeneous polynomials on ${\ell }_2$.

10 pages, Accepted for publication in the Proceedings of the AMS