Orlicz Spaces Expansion Model Stability And Geometric Properties

In this paper we mainly study the isomorphic stabilization of spreading models of Orlicz sequence spaces. Spreading model can display intuitively the structure of spaces, and it plays an important role similar to basis in the research work on the structure of spaces. Furthermore, it is a basic tool for discussing asymptotic problems, and it is used to prove the existence of strictly singular non-compact operator in Tsirelson spaces and to study the stabilization of equivalent norms in infinite dimensional subspaces.In chapter 1, we introduce the conception, significance and development of spreading models. In chapter 2, we first introduce some preliminary knowledge of basis in Banach spaces and of Orlicz sequence spaces. Afterwards, we recall some problems and known results of spreading models of Banach spaces, especially, Orlicz sequence spaces. In chapter 3, we focus on the isomorphic stabilization of spreading models in Orlicz sequence spaces, we give the relationship between the spreading model and its generating sequences in Orlicz sequence spaces. We also give a result related to isomorphic stabilization.