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Local rotundity structure of Calderón-Lozanovskii spaces |
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| Authors: | Henryk Hudzik |
| Affiliation: | a Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland b Institute of Mathematics of Electric Faculty, Poznah University of Technology, Piotrowo 3a, 60-965 Poznań, Poland c Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland |
| Abstract: | General results saying that a point x of the unit sphere S(E) of a Köthe space E is an extreme point (a strongly extreme point) [an SU-point] of B(E) if and only if ‖x‖ is an extreme point (a strongly extreme point) [an SU-point] of B(E+) and ‖x‖ is a UM-point (a ULUM-point) [nothing more] of E are proved. These results are applied to get criteria for extreme points and SU-points of the unit ball in Caldern-Lozanovski spaces which refer to problem XII from [5]. Strongly extreme points in these spaces are also discussed. |
| Keywords: | 46B20 46E30 46A45 |
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