从一致有界性到敛散边界
From Uniform Boundedness to the Boundary Between Convergence and Divergence
摘要：
本文引入了一致有界性原理的一个对偶，它不要求完备性，并给出了一个间接的检验集合有界性的方法。对偶原理，虽然已知的分析，尽管其应用在建立结果，如海林格-Toeplitz定理，往往是失踪的基本治疗的泛函分析。在例1中，我们指出了对偶原理和杜波依斯-雷蒙德关于序列收敛和发散之间边界的问题之间的联系。这个例子旨在说明为什么原则的陈述是自然的，并澄清原则主张什么和不主张什么。
英文摘要：
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.
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