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Hahn-Banach for metric functionals and horofunctions
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-04-07 , DOI: 10.1016/j.jfa.2021.109030 Anders Karlsson
中文翻译:
Hahn-Banach用于度量函数和完整函数
更新日期:2021-04-09
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-04-07 , DOI: 10.1016/j.jfa.2021.109030 Anders Karlsson
It is observed that a natural analog of the Hahn-Banach theorem is valid for metric functionals but fails for horofunctions. Several statements of the existence of invariant metric functionals for individual isometries and 1-Lipschitz maps are proved. Various other definitions, examples and facts are pointed out related to this topic. In particular it is shown that the metric (horofunction) boundary of every infinite Cayley graphs contains at least two points.
中文翻译:
Hahn-Banach用于度量函数和完整函数
可以观察到,Hahn-Banach定理的自然类似物对度量泛函有效,但对完整泛函则无效。证明了关于单个等式和1-Lipschitz映射不变度量功能的存在的几种说法。指出了与此主题相关的各种其他定义,示例和事实。特别地,表明每个无限的Cayley图的度量(函数)边界至少包含两个点。