离散度量空间的性质A和粗嵌入(英文)

Property A and Coarse Embedding of Discrete Metric Spaces

郁国梁教授对离散度量空间引进了性质A的概念,并且证明了具有性质A的离散度量空间能够粗嵌入到可分的希尔伯特空间.离散度量空间的粗嵌入与性质A之间的关系是一个大家都非常关注的问题.通过构造一系列能够粗嵌入到可分的希尔伯特空间但不具有性质A的离散度量空间,将Nowak的构造由非平凡的有限群推广到了任意非平凡的且能bi-Lipschitz粗嵌入到l1的离散度量空间上(如有限度量空间).

Yu Guoliang introduces property A of discrete metric spaces which guarantees the coarse embedding into Hilbert space. The relationship between property A and coarse embedding is an attractive problem. A class of metric spaces which can be coarsely embedded into Hilbert space without property A are constructed, which generalizes Nowak＇s construction in case of non-trivial finite groups to any non-trivial metric space which admits a bi-Lipschitz coarse embedding into l^l （e. g. finite metric spaces）.