一个弱*拓扑二分类及其在算子理论中的应用

IF 1.1 Q1 MATHEMATICS

Transactions of the London Mathematical Society Pub Date : 2013-02-28 DOI:10.1112/tlms/tlu001

Tomasz Kania, P. Koszmider, N. Laustsen

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引用次数: 9

摘要

用[0，ω1)表示具有有序拓扑的由所有可数序数组成的局部紧化Hausdorff空间，令C0[0，ω1)为在[0，ω1)上定义并最终消失的标量值连续函数的Banach空间。我们证明了C0[0，ω1]对偶空间的弱*‐紧子集是一致Eberlein紧的，或者它包含一个特定形式的有序区间[0，ω1]的同胚副本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A weak∗‐topological dichotomy with applications in operator theory

Denote by [0,ω1) the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let C0[0,ω1) be the Banach space of scalar‐valued, continuous functions which are defined on [0,ω1) and vanish eventually. We show that a weak * ‐compact subset of the dual space of C0[0,ω1) is either uniformly Eberlein compact, or it contains a homeomorphic copy of a particular form of the ordinal interval [0,ω1] .

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来源期刊

Transactions of the London Mathematical Society MATHEMATICS-

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

41 weeks