Metric duality for Abelian groups

被引：0
|
作者：
Niemiec, Piotr [1 ]
机构：
[1] Uniwersytet Jagiellonski, Wydzial Matematyki & Informatyki, Ul Lojasiewicza 6, PL-30348 Krakow, Poland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2025年 / 360卷
关键词：
Pontryagin's duality; LCA group; Invariant metric; Dual group; Reflexive topological Abelian group; Reflexive Banach space;
D O I：
10.1016/j.topol.2024.109155
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main aim of the paper is to introduce the concept of metric duality in the category of topological Abelian groups that extends the classical notion of duality for normed vector spaces and behaves quite nicely for LCA groups (equipped with nice metrics). In particular, it is shown that each Polish LCA group admits a reflexive proper metric and, more generally, all LCA groups possess reflexive (proper) metric structures. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
引用
收藏
页数：23
相关论文
共 50 条
12345