论文标题
从统一的界限到收敛与发散之间的边界
From Uniform Boundedness to the Boundary Between Convergence and Divergence
论文作者
论文摘要
在本文中，我们介绍了统一界原理的双重双重，该原理不需要完整性，并提供了测试集合界限的间接手段。二元原理虽然是分析师所知道的，尽管它在建立诸如hellinger-toeplitz定理之类的结果中的应用通常在功能分析的基本处理中通常缺少。在示例1中，我们指出了双重原理与杜波伊斯·里明德（Du Bois-Reymond）的问题之间的联系，即序列的融合和差异之间的边界。这个示例旨在说明为什么该原则的陈述是自然的，并阐明了原则主张及其所没有的主张。
In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing the boundedness of a set. The dual principle, although known to the analyst and despite its applications in establishing results such as Hellinger--Toeplitz theorem, is often missing from elementary treatments of functional analysis. In Example 1 we indicate a connection between the dual principle and a question in spirit of du Bois-Reymond regarding the boundary between convergence and divergence of sequences. This example is intended to illustrate why the statement of the principle is natural and clarify what the principle claims and what it does not.
