Some Geometric Properties Of The Orlicz Sequence Space Equipped With The Generalized Orlicz Norm

The Orlicz sequence space has various generalized forms, and the Orliczsequence space equipped with the p-Amemiya norm is the generation of the Orliczsequence space. With the development of the Orlicz sequence space, it has perfectedgradually. It is known that extreme points, strongly extreme points and λ property are important concepts and properties of the geometric theory of Banach space, theyare closely linked with the convexity.This thesis which is divided into three parts mainly studies on some geometricof properties of the Orlicz sequence space equipped with the p-Amemiya norm.Firstly, some basic properties of the Orlicz sequence space are studied. TheOrlicz sequence space is a kind of concrete Banach space, some important propertiesand theorems in this space are mainly introduced. By the deeply study of this space,the properties of this space can be extended to Orlicz sequence spaces equipped withthe p-Amemiya norm.Secondly, the basic properties of Orlicz spaces and sequence spaces equippedwith the p-Amemiya norm are introduced. Since the introduction of p-Amemiyanorm in2006, with the development of the Orlicz spaces, many properties andtheorems above spaces are obtained. Orlicz sequence space and Orlicz space areparallel development, in Orlicz sequence space equipped with the p-Amemiya norm,some important properties are also derived. The basic properties of Orlicz space andsequence space equipped with the p-Amemiya norm are reviewed in this section.Finally, λ property of Orlicz sequence space equipped with p-Amemiya normis discussed. As well known, λ property and the uniform λ property are importantproperties in Orlicz sequence space, while the Orlicz sequence spaces equipped withthe p-Amemiya norm is a classical generalization of the Orlicz sequence space. Inthis thesis, λ property and the uniform λ property are extended to the Orliczsequence space equipped with the p-Amemiya norm, which proved λ property isestablished, and the sufficient and necessary conditions for uniform λ property are given.