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Journal of Convex Analysis 21 (2014), No. 1, 167--177
Copyright Heldermann Verlag 2014

On Uniform Nonsquareness and Uniform Normal Structure in Banach Lattices

Stanislaw Prus
Institute of Mathematics, M. Curie-Sklodowska University, 20-031 Lublin, Poland

We give a sufficient condition for uniform nonsquareness of a Banach lattice in terms of the characteristic of monotonicity and the Riesz angle. For a Köthe space X we prove that orthogonal uniform convexity implies uniform normal structure and uniform nonsquareness both in X and X*.

Keywords: Uniform nonsquareness, uniform monotonicity, Riesz angle, orthogonal uniform convexity, uniform normal structure, fixed point property.

MSC: 46B20, 46B42, 46E30, 47H10

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