Radon–Nikodým property and Lau’s conjecture

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/proc/16884

Andrzej Wiśnicki

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引用次数: 0

Abstract

There is a long-standing problem, posed by A.T.-M. Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp. 121–129], whether left amenability is sufficient to ensure the existence of a common fixed point for every jointly weak ∗ ^{\ast } continuous nonexpansive semigroup action on a nonempty weak ∗ ^{\ast } compact convex set in a dual Banach space. In this note we discuss the current status of this problem and give a partial solution in the case of weak ∗ ^{\ast } compact convex sets with the Radon–Nikodým property.

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拉顿-尼科戴姆性质和刘氏猜想

A.T.-M. Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp.Lau [Fixed point theory and its applications, Academic Press, New York-London, 1976, pp.在本论文中，我们讨论了这一问题的现状，并给出了具有 Radon-Nikodým 性质的弱∗ ^{\ast } 紧凑凸集的部分解决方案。

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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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

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