Resumen de Relationships between monotonicity and complex rotundity properties with some consequences

H. Hudzik, A. Narloch

• It is proved that a point f of the complexification EC of a real Köthe space E is a complex extreme point if and only if |f| is a point of upper monotonicity in E. As a corollary it follows that E is strictly monotone if and only if EC is complex rotund. It is also shown that E is uniformly monotone if and only if EC is uniformly complex rotund. Next, the fact that |x|∈S(E+) is a ULUM-point of E whenever x is a C-LUR-point of S(EC) is proved, whence the relation that E is a ULUM-space whenever EC is C-LUR is concluded. In the second part of this paper these general results are applied to characterize complex rotundity of properties Calderón-Lozanovskiĭ spaces, generalized Calderón-Lozanovskiĭ spaces and Orlicz-Lorentz spaces.