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

• Francisco Javier García-Pacheco ^[1]
  1. [1] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 54, Nº. 1, 2013, págs. 69-82
• Idioma: inglés
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• Resumen

  • 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.