关于弱$^*$导集是适当且范数稠密的子空间

IF 0.7 3区 数学 Q2 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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