Banach空间上的有界拓扑及其在经济中的一些应用 理论述评

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摘要翻译：
回顾了关于实Banach空间上拓扑T的有界和凸有界变体bT和cbT的已知结果。重点讨论了对偶Banach空间P*上的弱拓扑和Mackey拓扑T=w(P*,P）和T=m(P*,P）的情形。凸有界Mackey拓扑，cbm(P*,P）与m(P*,P）等价。对于bm(P*,P）,我们推测它严格地强于m(P*,P）或等价地不是向量拓扑（除非P是自反的）。指出了有界Mackey拓扑和有界弱拓扑在经济理论中的一些用途及其应用。讨论了一般Banach空间Y上的有界弱拓扑和紧致弱拓扑bw(Y,Y*)和kw(Y,Y*)及其凸变体（cbw和ckw）。
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英文标题：
《Bounded topologies on Banach spaces and some of their uses in economic
  theory: a review》
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作者：
Andrew J. Wrobel
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最新提交年份：
2020
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分类信息：

一级分类：Mathematics        数学
二级分类：Functional Analysis        功能分析
分类描述：Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory
Banach空间，函数空间，实函数，积分变换，分布理论，测度理论
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  Known results are reviewed about the bounded and convex bounded variants, bT and cbT, of a topology T on a real Banach space. The focus is on the cases of T = w(P*, P) and of T = m(P*, P), which are the weak* and the Mackey topologies on a dual Banach space P*. The convex bounded Mackey topology, cbm(P*, P), is known to be identical to m(P*, P). As for bm(P*, P), it is conjectured to be strictly stronger than m(P*, P) or, equivalently, not to be a vector topology (except when P is reflexive). Some uses of the bounded Mackey and the bounded weak* topologies in economic theory and its applications are pointed to. Also reviewed are the bounded weak and the compact weak topologies, bw(Y, Y*) and kw(Y, Y*), on a general Banach space Y, as well as their convex variants (cbw and ckw).
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PDF链接：
https://arxiv.org/pdf/2005.05202

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关键词：Banach NAC BAN Contribution Applications theory bounded Banach cbm 述评