巴拿赫空间是如何产生的

How was the Banach Space Generated?

通过讨论巴拿赫空间概念的优先权,提出了判定巴拿赫空间概念形成的四个条件:导致巴拿赫空间概念形成的具体数学问题、范数的定义、空间的完备性及其在积分方程的应用。通过比较巴拿赫和里斯的工作,发现了里斯已经在具体空间中给出了巴拿赫空间概念形成所需的全部条件,为巴拿赫空间一般概念的建立奠定了基础。

Through the discussion of the priority of Banach Space, we can put forward four conditions of the formation of the concept of Banach Space, such that, the specific mathematical problems leading to the formation of the concept of Banach space, the definition of norm, the completeness of the Banach Space and the application into the integral equations. By comparing the work of Banach and Riesz, we can find that Riesz has given the concept of Banach space in the specific space, which lays the foundation for the establishment of the general concept of Banach Space.