Hahn-Banach定理的形成

The formation of Hahn-Banach theorem

在探讨Hahn-Banach定理的产生过程中,用原始文献分析法,对延拓思想的内涵进行系统分析。得出里斯(Riesz,1880—1956)提出了延拓方法,并将延拓方法应用于Lp空间,黑利(Helly,1884—1943)证明了延拓方法的可行性,哈恩(Hahn,1879—1934)推广了延拓思想。里斯定理、黑利引理和黑利关键不等式是Hahn-Banach定理完善的基础。最终得到里斯和黑利创造了Hahn-Banach定理,哈恩和巴拿赫(Banach,1892—1945)完善了这个定理。

In this paper, the production process of Hahn-Banach theorem is explored Starting from the original docu- ments, the ideological connotation of continuation is systematically analyzed. Then it shows that Riesz proposed the thought of continuation, Helly proved the thought, Hahn extended the thought, Banach completed the thought. Riesz theorem, Helly lemma and Helly key inequality are the base of the Hahn-Banach theorem. In the end, the conclusion is drawn that Riesz and Helly created the Hahn-Banach theorem, Hahn and Banach made the theorem more perfect.