Revistes Catalanes amb Accés Obert (RACO)

A dual property to uniform monotonicity in Banach lattices

W. Kurc


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.

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