论文标题
关于Mazur旋转问题及其多维版本
On Mazur rotations problem and its multidimensional versions
论文作者
论文摘要
本文是一项与Banach Space理论中经典未解决问题有关的调查，该研究出现在1932年Banach著名的书中，被称为Mazur Rotations问题。尽管这个问题似乎非常困难且相当抽象，但它的研究阐明了Banach空间的规范对称性的重要性，有时证明了有时与重态的理论和功能分析中的可怜性的意外联系，以及拓扑组理论和表述理论，以及与不舒张的领域以及Fraïssé理论和Ramsey理论和Ramsey Theory和Ramsey理论的发展，并导致了独立于MAZUR的概念。这项调查重点是2000年以后发表的结果，强调了过去十年中开发的两项研究。第一个是研究Mazur旋转问题的大概版本的各个方面的研究，尤其是在Lebesgue Spaces LP的情况下。第二个涉及Mazur旋转问题和相关结果的多维公式的最新发展。还包括一些新的结果。
The article is a survey related to a classical unsolved problem in Banach space theory, appearing in Banach's famous book in 1932, and known as the Mazur rotations problem. Although the problem seems very difficult and rather abstract, its study sheds new light on the importance of norm symmetries of a Banach space, demonstrating sometimes unexpected connections with renorming theory and differentiability in functional analysis, with topological group theory and the theory of representations, with the area of amenability, with Fraïssé theory and Ramsey theory, and led to development of concepts of interest independent of Mazur problem. This survey focuses on results that have been published after 2000, stressing two lines of research which were developed in the last ten years. The first one is the study of approximate versions of Mazur rotations problem in its various aspects, most specifically in the case of the Lebesgue spaces Lp. The second one concerns recent developments of multidimensional formulations of Mazur rotations problem and associated results. Some new results are also included.
