对偶Banach空间中凸集的弱$^*$闭包和导集

IF 0.7 3区数学 Q2 MATHEMATICS

Studia Mathematica Pub Date : 2021-12-09 DOI:10.4064/sm211211-25-6

M. Ostrovskii

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引用次数: 2

摘要

摘要：本文致力于Banach和Mazurkiewicz提出的子空间弱导集理论的凸集对应。主要结果如下：对于每个非弹性Banach空间X和每个可数后继序数α，X中存在一个凸子集a，使得α是阶α的弱导集与a的弱闭包重合的最小序数。这一结果扩展了Ostrovski（2011）和Silber（2021）关于弱导集的先前已知结果。

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Weak$^*$ closures and derived sets for convex sets in dual Banach spaces

Abstract: The paper is devoted to the convex-set counterpart of the theory of weak derived sets initiated by Banach and Mazurkiewicz for subspaces. The main result is the following: For every nonreflexive Banach space X and every countable successor ordinal α, there exists a convex subset A in X such that α is the least ordinal for which the weak derived set of order α coincides with the weak closure of A. This result extends the previously known results on weak derived sets by Ostrovskii (2011) and Silber (2021).

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来源期刊

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

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.