Some Properties Of Orlicz Space Equipped With The P-Amemiya Norm

According to the requirement of various theories and application, there are many generalizations of Orlicz spaces. The Orlicz spaces equipped with the p-Amemiya norm is a generalization among the number. Locally convexity, H property and the dual spaces of Orlicz spaces equipped with the p-Amemiya norm are studied. This thesis consists of four parts. The main results are as follows:First of all, it is reviewed that developing course of the theory and geometry of Orlicz spaces during more than 80 years studies. Moreover, the pioneer's main research results are evaluated and summarizied, and the background and significance of each part in this thesis are shown.Second, the dual spaces of Orlicz spaces equipped with the p-Amemiya norm which help us study the space better is studied. The dual space is also an Orlicz spaces equipped with the p-Amemiya norm. The structures of the dual spaces of Orlicz spaces equipped with the p-Amemiya norm are discussed.Third, local convexity plays an important role in the geometry of Banach spaces. Many scholars had done an in-depth study of locally uniform rotundity, weakly locally uniform rotundity and compactly locally uniform rotundity of Orlicz spaces equipped with the Luxemburg norm and the Orlicz norm, and have obtained a lot of good results. In this thesis, the necessary and sufficient conditions for locally uniform rotundity, weakly locally uniform rotundity and compactly locally uniform rotundity in Orlicz spaces equipped with the p-Amemiya norm are shown.Finally, H property which implies many good properties, is also important in the geometry of Banach spaces. A good many scholars at home and abroad have done an in-depth study of H property of Orlicz spaces equipped with the Luxemburg norm and the Orlicz norm, and have got many good results. In this thesis, the necessary and sufficient conditions for H property of Orlicz spaces equipped with the p-Amemiya norm are given.