Equivalence of topologies and Borel fields for countably-Hilbert spaces
Equivalence of topologies and Borel fields for countably-Hilbert spaces
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DOI：
10.1090/s0002-9939-05-08219-5
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发表时间：
2005-08
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影响因子：
--
通讯作者：
Jeremy J. Becnel
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文献类型：
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作者：
Jeremy J. Becnel
我们研究了置于可数赋范空间的对偶上的主要拓扑--弱、强和归纳--以及由这些拓扑生成的场。特别地，我们证明了对于某些可数-Hilbert空间，强拓扑与归纳拓扑重合，由弱、强、归纳拓扑生成的场是等价的。1.引言和目的本文研究了赋可数范空间的对偶上的弱、强、归纳拓扑。我们看到，在某些条件下，强拓扑和归纳拓扑重合(并且也等价于后面介绍的Mackey拓扑)。我们还检查和比较了由这些拓扑生成的-场，以发现在合理的条件下，所有的-场实际上是等价的。
We examine the main topologies—weak, strong, and inductive— placed on the dual of a countably-normed space and the -fields generated by these topologies. In particular, we prove that for certain countably-Hilbert spaces the strong and inductive topologies coincide and the -fields generated by the weak, strong, and inductive topologies are equivalent. 1. Introduction and Objectives In this paper we study the weak, strong, and inductive topologies on the dual of a countably-normed space. We see that under certain conditions the strong and inductive topologies coincide (and are also equivalent with the Mackey topology, which is introduced later). We also examine and compare the -fields generated by these topologies to see that under reasonable conditions all the -fields are in fact equivalent.