summary:In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space $X$ can be characterized through the behaviour of its weakly-$\ast $ unconditionally Cauchy series in $X^\ast $.
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机译：摘要：在本文中，通过弱无条件柯西级数的行为，我们获得了赋范空间完整性的两个新特征。我们还证明了赋范空间$ X $的桶形性可以通过其弱$$ ast $无条件柯西级数在$ X ^ \ ast $中的行为来表征。
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