Monotonicity and rotundity properties in banach lattices


Some general results on geometry of Banach lattices are given. It is shown among others that uniform rotundity or rotundity coincide to uniform or strict monotonicity, respectively, on order intervals in positive cones of Banach lattices. Several equivalent conditions on uniform and strict monotonicity are also discussed. In particular, it is proved that in Banach function lattices uniform and strict monotonicity may be equivalently defined on orthogonal elements. It is then applied to show that p-convexification E(p) of E is uniformly monotone if and only if E possesses that property. A characterization of local uniform rotundity of Calderón-Lozanovskii spaces is also presented. © 2000 Rocky Mountain Mathematics Consortium.

Publication Title

Rocky Mountain Journal of Mathematics