关于弱$^*$导集是适当且范数稠密的子空间

Pub Date : 2022-03-01 DOI:10.4064/sm220303-29-4
Zdenvek Silber
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引用次数: 0

摘要

我们研究了子空间的迭代弱*导集的长链,即有界网的所有弱*极限的集,以及倒数第二个弱*导集合是对偶的适当范数稠密子空间的附加性质。我们推广了Ostrovski的结果,证明了在包含具有可分对偶的无穷维子空间的任何非拟自反Banach空间的对偶中,我们可以为任何可数后继序数α找到一个子空间,其阶α的弱*导集是适当的且范数稠密的。
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On subspaces whose weak$^*$ derived sets are proper and norm dense
We study long chains of iterated weak∗ derived sets, that is sets of all weak∗ limits of bounded nets, of subspaces with the additional property that the penultimate weak∗ derived set is a proper norm dense subspace of the dual. We extend the result of Ostrovskii and show, that in the dual of any nonquasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual, we can find for any countable successor ordinal α a subspace, whose weak∗ derived set of order α is proper and norm dense.
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