Some Problems About James Space And The Operators On It

Master thesis "some problems about James space and the operators on it" is the organic combinative results of the study on the theory of Banach space and the theory of functional analysis.There are three chapters in the paper.In chapter one we introduce the history of the study of James space.We specify the prerequisites needed in the following chapters.Moreover,we obtain some new sufficient and necessary conditions which make a Schauder basis be shrinking basis and which make a shringking basis have special property.And the study trends of James space are also prospected.In chapters two,we study the structure of James space.We show that James space is not isomorphic to any finite dimensional p-block decomposition space.And we get some further results on the structure of the complementary subspaces of James space.Chapter three mainly studies the operators on James space.We extend Stampfli's theorem to James spacc——namely,for any operator T in B(J),there is a compact operator K so thatσ(T+K)is minimal.As a corollary, every Riesz operator on James space has West decomposition.The two results are main works of this paper.They give an affirmative answer to the famous problem of decomposition theory of operators in the case of James space.We also get some results on operator ideals and Boolean algebra of projections in James space.