The structure of compact disjointness preserving operators on continuous functions

YingFen Lin Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43681

Mathematische Nachrichten, 282, (7), 1009-1021, 2009.7
Let <i>T</i> be a compact disjointness preserving linear operator from <i>C</i><sub>0</sub>(<i>X</i>) into <i>C</i><sub>0</sub>(<i>Y</i>), where <i>X</i> and <i>Y</i> are locally compact Hausdorff spaces. We show that <i>T</i> can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, <i>T</i> = <sub><i>n</i> </sub> <i></i> <i>h<sub>n</sub></i> for a (possibly finite) sequence {<i>x<sub>n</sub></i> }<sub><i>n</i> </sub> of distinct points in <i>X</i> and a norm null sequence {<i>h<sub>n</sub></i> }<sub><i>n</i> </sub> of mutually disjoint functions in <i>C</i><sub>0</sub>(<i>Y</i>). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator ( 2009 WILEYVCH Verlag GmbH &amp; Co. KGaA, Weinheim)
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@inproceedings{yingfen2009the,
  title={The structure of compact disjointness preserving operators on continuous functions},
  author={YingFen Lin, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210447262371210},
  booktitle={Mathematische Nachrichten},
  volume={282},
  number={7},
  pages={1009-1021},
  year={2009},
}
YingFen Lin, and Ngai-Ching Wong. The structure of compact disjointness preserving operators on continuous functions. 2009. Vol. 282. In Mathematische Nachrichten. pp.1009-1021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210447262371210.
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