Some Properties In Orlicz And Cesaro-Orlicz Sequence Spaces

As we known, the concept of Orlicz space was introduced by W. Orlicz early in 1932. It is an important extension of the notion of classical Lebesgue spaces Lp and l p. As a concrete Banach space, it is applied in best approximation, and optimal control problems. So, it is important to research the geometrical problems of Orlicz spaces.Some geometrical properties of Orlicz spaces and Cesaro-Orlicz sequence spaces equipped with Luxemburg norm are investigated in this thesis. The main results of this thesis are summarized as following:Chapter 1 Introduction: The developing course of Orlicz spaces during more than 60 years is reviewed, the main existent results and the basic knowledge of Orlicz spaces are introduced, and then, the background and significance of the main contents discussed are summarized.Chapter 2λ- sproperty in Orlicz spaces: Theλ- s property in Orlicz spaces is discussed and the fact that for any Orlicz function, the Orlicz space has theλ- s property is proved, at last, the discriminant condition of uniformλ- s property is given.Chapter 3 Some properties in Cesaro-Orlicz sequence spaces: In this chapter, the dual spaces of the Cesaro-Orlicz sequence spaces and the criteria for the extreme point are studied and the sufficient and necessary condition of which the spaces has theλ- property and the uniformλ- property is given by the above results.