Arens regularity of some bilinear maps

• Gordji, M. Eshaghi ^[1]
  1. [1] Semnan University

     Semnan University

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 28, Nº. 1, 2009, págs. 21-26
• Idioma: inglés
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• Resumen

  • Let H be a Hilbert space. we show that the following statements are equivalent: (a) B(H) is finite dimension, (b) every left Banach module action l : B(H)×H → H, is Arens regular (c) every bilinear map f : B(H)*→ B(H) is Arens regular. Indeed we show that a Banach space X is reflexive if and only if every bilinear map f : X* × X → X* is Arens regular.