作为Fréchet和DF-空间的张量积产生的连续函数的加权PLB-空间
Weighted PLB-spaces of continuous functions arising as tensor products of a Fréchet and a DF-space
摘要：
连续函数的加权巴拿赫空间的可数归纳极限的可数投射极限，即所谓的PLB-空间，最近已经由Bethen，Bierstedt和Bonet研究，他们根据定义的双权序列分析了局部凸性质。我们补充他们的结果，考虑一个定义序列，这是两个单一的序列的产品。通过将这两个序列分别与加权Fréchet相关联，连续函数的LB-空间或与两个加权Fréchet空间（通过取其中一个序列的倒数）的关系，我们导出了PLB-空间作为Fréchet和DF-空间的张量积的表示，并给出了Fréchet空间的不变量（DN）和（$Ω$）与PLB-空间的局部凸性质之间的联系.上述张量积的乘积。
英文摘要：
Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet, who analyzed locally convex properties in terms of the defining double sequence of weights. We complement their results by considering a defining sequence which is the product of two single sequences. By associating these two sequences with a weighted Fréchet, resp. LB-space of continuous functions or with two weighted Fréchet spaces (by taking the reciprocal of one of the sequences) we derive a representation of the PLB-space as the tensor product of a Fréchet and a DF-space and exhibit a connection between the invariants (DN) and ($Ω$) for Fréchet spaces and locally convex properties of the PLB-space resp. of the forementioned tensor product.
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