Projective and injective limits of weakly compact sequences of locally convex spaces
Projective and injective limits of weakly compact sequences of locally convex spaces
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局部凸空间弱紧序列的射影和单射极限
DOI：
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发表时间：
1967
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通讯作者：
H. Komatsu
中科院分区：
文献类型：
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作者：
H. Komatsu
Silva [15]和Raikov [12] [13]研究了局部凸空间的紧序列的投射极限和内射极限，揭示了用这些极限表示的局部凸空间的显著性质。然而，他们似乎没有注意到，这些空间正是Grothendieck [5]所讨论的Fr 'echet Schwartz空间及其强对偶空间。我们将他们的结果推广到局部凸空间的弱紧序列的极限空间，并证明了几乎所有重要的性质都保持不变。除了闭值域定理和（DF）空间的定义外，我们只假定Bourbaki [1]的文本。具有（一一）连续线性映射的局部凸空间的投射（内射）序列：
Silva [15] and Raikov [12] [13] studied projective and injective limits of compact sequences of locally convex spaces and revealed remarkable properties of the locally convex spaces expressed as those limits. However, they do not seem to have noticed at first that those spaces are exactly the Fr\’echet Schwartz spaces and their strong dual spaces discussed by Grothendieck [5]. We extend their results to the limit spaces of weakly compact sequences of locally convex spaces and show that almost all important properties are preserved. We presuppose only the text of Bourbaki [1] except for the closed range theorem and the definition of (DF) spaces. A projective (injective) sequence of locally convex spaces with (one-one) continuous linear mappings: