The Formation Of The Theory Of Banach Space From The Integral Equation

The theory in Banach space for integral equations is the one which researches the structure of Banach space and the nature of integral equations, it has not only the intimate relationship with mathematical branches, but also very important application in many aspects. So, it has important theoretical significance and application value for research on the history of this theory. This paper is built on the original literature and literatures about correlational research.'Why Mathematics' is as the research basis, and it has a systematic study on how the theory for integral equations impact the formation of theory in Banach space. And it has the results as follows:1. By analyzing the formation and developing process of eigenvalue theory for integral equations systematically, it can be found that the eigenvalue problem has an important impact on the development of the theory in Banach space, and it is the key factor of this development.2. For the diversity in application of this theory, it is easy to know that the reason for its formation is various. It shows that' moment problem'is a significance reason for the formation of theory in Banach space for which it has been studied systematically.3. It researches the work of all mathematicians in aspect of normed linear space deeply and particularly, and investigates the history of the theory in Banach space in detail. At the same time, it determines the importance of priority and presents the judging criteria:a specific mathematical problem, the concept for complete normed space is certain, the application in integral equations. And it shows that Reese's work satisfied all the judging criteria on the formation of theory in Banach space. A important influence is presented here. In addition, it analyzes the effect of the social factors such as politics, nation and teacher-student relations which indicates the inevitability for the formation of theory in Banach space.4. It shows the fluence of this theory in every field, and gives a clear explanation by discussing the relationship between this theory and some basic theories. Morever, it establishes its crucial position among all mathematical theories.