Abstract
We first prove that if x is an element on the unit sphere of arbitrary Köthe space E, x is strickly positive μ-a.e. and x is an LM-point, then x is an UM-point. Criteria for lower and upper monotone points in Calderón-Lozanovskiǐ spaces E ϖ are presented. Points of lower local uniform monotonicity and upper local uniform monotonicity in E ϖ are also considered. Some sufficient conditions and necessary conditions for these properties of a given point x in S( E ϖ +) are given.
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