Banach Space Expansion Model Structure

The thesis mainly study the structure of countable spreading models of an Orliczsequence space. The research of spreading models' theory plays an important rolein the structure of Banach spaces. The study concerning spreading models' theorycontains the following two aspects: Firstly, through a Banach space with somespecial properties to study the structure of spreading models; Secondly, though thespreading models of a Banach space which have some special properties to researchit's structure. The emergence and development of spreading models theory enrichthe functional analysis theory, and expand the application field of functional analysis.The first chapter introduces spreading models' background, meaning, developmentand contents of main study; Some theory related to spreading models and recentlyannounced meaningful thesis-one of them is regarding coincidence between speadingmodel of an Orlicz sequence space and symmetric sequences-are given in the second; The third part chapter we give some related conceptions on spreading models,symmetric basic sequence and generated block basis, and obtain the main result: Ifa set of spreading model generated by weakly null sequences in Banach space withsymmetric basis is countable by means of equivalence, then it contains a spreadingmodel that is isomorphic topor c0; Last is conclusion part, and we raise someproblems that can be done after this paper.