Some Geometrical Property Of Musielak-Orlicz Sequence Spaces

According to the requirement of various theories and application, there are many generalizations of Orlicz space. Musielak-Orlicz space is a common generalization. This thesis investigates mainly the locally (weakly) uniform rotundity and monotone points of Musielak-Orlicz sequence space. It consists of five parts. The main results of the thesis are summarized as following:Chapter 1 Introduction :It is reviewed that developing course of the theory and geometry of Orlicz sequence space during more than 60 years studies. Moreover, it is evaluating and summarizing the pioneer's main research results, and showing the background and significance of the content of each part in this thesis.Chapter 2 On the locally (weakly) uniform rotundity of Musielak-Orlicz sequence spaces: Rotundity is important property in the geometry of Banach space. In this paper, criterion that Musielak-Orlicz sequence spaces equipped with the Orlicz norm and Luxemburg norm is locally (weakly) uniformly rotund was discussed in detail. Moreover, we get the sufficient and necessary condition of them.Chapter 3 Monotone Points in Musielak-Orlicz sequence spaces: The role of monotonicity in Banach much like the rotundity in Banach spaces. In this paper, the conceptions of the upper (lower) monotone points and upper (lower) locally monotone point are introduced, and the criteria of upper (lower) monotone point and upper (lower) locally monotone point of Musielak-Orlicz sequence spaces are given. Moreover, from the relation of point property and space property, criteria of space monotonicity are given as corollary.