Semi-ordered Set Sp_w (x) The Structure Of The Problem

The study of the structure of Banach spaces and its subspaces is an observational problem in the area of functional analysis.In recent years,the advent of the theory on spreading models not only provides a new way of thinking and methods for understanding and solving the above problems,but also has important meaning in the operator's existence and distortion of Banach space.The spreading model may be the subspace of Banach space,or may also be a new space which has similar and better structure than the subspace and infintely approximated to the subspace,so the research of the spreading model theory can help us more effectively to understand the Banach space itself.In this paper,we study the partial order structures of the spreading models of Banach space X generated by normalized weakly null sequences.The first chapter introduces spreading models' background,significance and development.Some basic conceptions and related results on Banach space and Orlicz sequence space are given in the second chapter,and makes a sufficient preparation for the next chapter. The third part we mainly prove the equivalence relationship between the two forms of definitions and the existence for a separable infinite dimensional Banach space's spreading model,then we construct a specific Orlicz sequence space l_M such that |SP_w(lM)| = 2 and give the relevant conclusions of order-isomorphism in spreading model.In the end of the paper,we make some conclusions and put forward some problems.