Some Heredities Of The Quotient Space And Direct Sum Banach Space

Some geometrical properties of quotient space, G-Space with quotient space, E~*Space with quotient space, some geometrical properties of ? -Direct Sumsare investigated in this thesis. The main results of the thesis are summarized as following:In the first place, in the Introduction, It is reviewed that developing course of the theory of Banach spaces and the pioneer's main research results during more than years. Moreover, it is summarizing the construction of quotient spaces and showing the back ground and significance of the content of each part in this thesis.Sencondly, Some geometrical properties of quotient space in the chapter, k uniformly convexity , Nearly uniformly convexity , Midpoint locally uniform convexity on the quotient space, and gives the relevant proof. Suppose X is k uniformly convexity Banach space and M the approximation close space by X , then the quotient space X / Mis also K uniformly convexity. Furthermore, G-Space with quotient space, E~*Space with quotient space in the chapter G-space concepts are first proposted, the nature of G-space is studied, discussed the quotient of G-space is still G-space; Then study Some geometrical properties of E~*-space and its quotient.Given the relevant necessary and sufficient conditions to prove.Finally, ? -Direct Sums Heredityin zhe chapter, Midpoint locally uniform convexity and Midpoint locally K-uniform convexity has been the relationship between the convexity , Some geometrical properties of ? -Direct Sumsare investigated in this thesis, and relerant proofs are gived.