Resumen de Translations, norm-attaining functionals, and elements of minimum norm

Francisco Javier García Pacheco

• In this paper we continue a work that James started in 1971 about norm-attaining functionals on non-complete normed spaces by proving that every functional on a normed space is norm-attaining if and only if every proper, closed, convex subset with non-empty interior can be translated to have a non-zero, minimum-norm element. We also study this type of spaces when they are non-complete. Finally, we consider translations and elements of maximum norm.