Geometry of banach spaces with diameter two properties and octahedral norm
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AuthorRueda Zoca, Abraham
Universidad de Granada
DepartamentoUniversidad de Granada. Programa de Doctorado en Física y Matemáticas
Rueda Zoca, Abraham. Geometry of banach spaces with diameter two properties and octahedral norm. Granada: Universidad de Granada, 2019. [http://hdl.handle.net/10481/57262]
SponsorshipTesis Univ. Granada.; MECD FPU16/00015.; Proyecto MINECO MTM2015-65020-P; Grupo de Investigación de la Junta de Andalucía FQM- 0199.; Grupo de Investigación de la Junta de Andalucía FQM- 0185.
The aim of this dissertation is to analyse and solve several problems in the theory of diameter two properties, octahedrality, and to take advantage of the strong connection between the diameter two properties and the octahedrality of the norm to study new examples of Banach spaces whose norm is octahedral. The content of the thesis is organised in three chapters: -Chapter 1: It is devoted to provide basic background about the diameter two properties, connections with different properties of the geometry of Banach spaces, classical examples of Banach spaces with the diameter two properties and different stability results by taking classical l_p-sums. -Chapter 2: It is devoted to analysing different problems related to the diameter two properties and to present the strong connections between the diameter two properties and the octahedral norms. Chapter 3: It is devoted to analysing the octahedrality of the norm of two different kind of Banach spaces.