Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Banach spaces and their linear operator theory.

Some Geometrical Properties and Moduli of Banach Spaces

Author HeZuo
Tutor CuiYunAn
School Harbin University of Science and Technology
Course Basic mathematics
Keywords Endpoint Consistent lambda nature Non- party constant Generalized non- party constant Fixed point
CLC O177.2
Type Master's thesis
Year 2007
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In the past more than 70 years , the study of the geometric properties of generalized Lebesgue spaces has achieved a lot of results , however, research has focused on the overall nature of the space , and the local nature of the space as well as a variety of geometric constant value but did not get enough attention. On the other hand , the non constant as early as 1971 to get the promotion, so far, however , the generalized nonsquare constant research does not have much . This paper focuses on generalized Lebesgue spaces in certain geometric properties and geometric constants , and through a detailed study of the nature of the generalized nonsquare constant promotion of some of the conclusions on the non- party constant , and some new conclusions . First of all, this paper reviews the generalized Lebesgue spaces and generalized non - constant process of development , summarizes the key findings of the previous , and demonstrate the content discussed in this article the basic knowledge , background and significance . Second, the paper characterizes the generalized Lebesgue spaces endpoints and strict convexity , necessary and sufficient conditions for generalized Lebesgue spaces with consistent lambda nature . As a corollary , strictly convex and consistent lambda nature are equivalent in the generalized Lebesgue spaces . Geometric constant calculation , promotion Clarkson inequality , when p (x) satisfies p ... - ≥ 2 or 1 < p ~~ - ≤ P ~ ≤ 2 non- Fang constant in generalized Lebesgue spaces in the exact value . Finally , this paper presents a generalized non- party constant equivalent representations of the upper and lower bounds , has been generalized nonsquare constant ι_p . The value of the space , and to study the relationship between a the generalized nonsquare constant and non - party constant . As a corollary , this paper gives the the generalized nonsquare constant and uniformly convex and uniformly nonsquare relationship , and then get some sufficient conditions for the fixed point property . On the other hand , the article discusses J ( t , X ) and J ( t , X * ) the relationship between the given J ( t , X ) S ( t , X ) upper and lower bounds , to discuss the J ( t , X ) and the relationship between the Banach - Mazur distance , and further study the relationship between J ( t , X ) with the same formal structure .

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