We show how to construct non-locally convex quasi-Banach spaces X whose dual separates the points of a dense subspace of X but does not separate the points of X. Our examples connect with a question raised by Pietsch (Rev Mat Complut 22(1):209–226, 2009) and shed light into the unexplored class of quasi-Banach spaces with nontrivial dual which do not have sufficiently many functionals to separate the points of the space.

中文翻译：

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关于Banach信封的“哲学”问题

我们将展示如何构建非局部凸准Banach空间X，其双密集的子空间的点中隔离X但是点不开X。我们的示例与Pietsch（Rev Mat Complut 22（1）：209–226，2009）提出的问题有关，并阐明了具有非平凡对偶且没有足够多泛函来分离点的拟Banach空间的未探索类的空间。