%0 Journal Article 
%A García Pacheco, Francisco Javier
%T On sup-and inf-attaining functionals
%D 2024
%@ 2391-5455
%U http://hdl.handle.net/10498/36917
%X Reflexivity is characterized by the weak-compactness of the unit ball. The weak-compactness of bounded, closed, and convex sets is characterized through sup-attaining functionals in view of the famous James’ theorem. The aim of this mathematical note is to provide the construction of bounded, closed, and convex subsets for which there exists a functional attaining its supremum on such a set but not its infimum. This construction leads to a characterization of reflexivity in the category of normed spaces and a characterization of full norm-attainment also in the category of normed spaces.
%K reflexivity
%K norm-attaining operator
%K Bishop-Phelps theorem
%K supporting vector
%~ Universidad de Cádiz