Disjointness preserving shifts on C0 (X)

Li-Shu Chen Jyh-Shyang Jeang Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43678

Journal of mathematical analysis and applications, 325, (1), 400-421, 2007.1
We study disjointness preserving (quasi-) n-shift operators on C 0 (X), where X is locally compact and Hausdorff. When C 0 (X) admits a quasi-n-shift T, there is a countable subset of X= X{} equipped with a tree-like structure, called -tree, with exactly n joints such that the action of T on C 0 (X) can be implemented as a shift on the -tree. If T is an n-shift, then the -tree is dense in X and thus X is separable. By analyzing the structure of the -tree, we show that every (quasi-) n-shift on c 0 can always be written as a product of n (quasi-) 1-shifts. Although it is not the case for general C 0 (X) as shown by our counter examples, we can do so after dilation.
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@inproceedings{li-shu2007disjointness,
  title={Disjointness preserving shifts on C0 (X)},
  author={Li-Shu Chen, Jyh-Shyang Jeang, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210358369203207},
  booktitle={Journal of mathematical analysis and applications},
  volume={325},
  number={1},
  pages={400-421},
  year={2007},
}
Li-Shu Chen, Jyh-Shyang Jeang, and Ngai-Ching Wong. Disjointness preserving shifts on C0 (X). 2007. Vol. 325. In Journal of mathematical analysis and applications. pp.400-421. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210358369203207.
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