Relationships between monotonicity and complex rotundity properties with some consequences

• Autores: H. Hudzik, A. Narloch
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 2, 2005, págs. 289-306
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.