A dual property to uniform monotonicity in Banach lattices

• Autores: W. Kurc
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 44, Fasc. 1-3, 1993, págs. 155-166
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • For Banach lattices $X$ with strictly or uniformly monotone lattice norm dual, properties (o)-smoothness and (o)-uniform smoothness are introduced. Lindenstrauss type duality formulas are proved and duality theorems are derived. It is observed that (o)-uniformly smooth Banach lattices $X$ are order dense in $X^{\ast\ast}$. An application to an optimization problem is given.

• Referencias bibliográficas
  • C. Aliprantis, O. Burkinshaw, Positive Operators, Academic Press Inc., 1985.
  • G. Birkhoff, Lattice Theory, Providence, RI, 1967.
  • H. Hudzik, W. Kurc, Monotonicity of Musielak-Orlicz spaces equipped with the Orlicz norm (to appear).
  • W. Kurc, Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation, Journal of Approximation Theory 69(2),...
  • W. Kurc, Strictly and uniformly monotone sequential Musielak-Orlicz spaces (to appear).
  • W. Kurc, Extreme points of the unit ball in Orlicz spaces of vector-valued functions with the Ameniya norm, Mathematica Japonica 38(2), (1993),...
  • W. Kurc, Musielak-Orlicz spaces with order smooth norms, (to appear).
  • P. Nieberg, Banach Lattices, Springer Verlag, 1991.