Some Geometry Properties Of Orlicz Spaces And The Dual Spaces

The applications of the theories in Orlicz spaces are widely used, it is historically necessary for the study from L₂ and L_p( p≥1) to Orlicz spaces. As a class of specific Banach space, many classes of Banach spaces are covered by Orlicz spaces. Therefore, its various properties are visual materials for general Banach spaces. The more we reserve its knowledge the more appropriate for the applications. In recent years, many scholars both in motherland and abroad did research in generalized Orlicz spaces, and obtained many good results. The dual space of Orlicz space is also an important class of Banach spaces. We can deeply know about Orlicz space by studing the properties of its dual spaces. In order to enrich the theories of Orlicz spaces, people tried to do some parallel extension about some conclusions which are right in Orlicz spaces to its dual spaces.The thesis mainly consists of the following three parts:First of all, it is about some basic properties of Orlicz spaces. In this paper, we mainly gave the definition forΔ₂condition that is satisfied by a point, and in sense of this definition we obtained several basic properties in Orlicz space.The criteria forσextreme points in Orlicz was studied secondly. There are many important properties for points in Orlicz space. We gave the criteria for the nearly strict convexity of Orlicz spaces by the study ofσextreme points.Finally, we did research about theK extreme points in the dual space of Orlicz spaces equipped with the Luxemburg norm, and we also studied the criteria for extreme points in the dual space of Orlicz spaces equipped with the Orlicz norm...