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A dual property to uniform monotonicity in Banach lattices.

W. Kurc — 1993

Collectanea Mathematica

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**. An application to an optimization theorem is given.

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