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A Banach-Stone theorem for Riesz isomorphisms of Banach lattices

Jin Chen Zi Chen Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43663

Proceedings of the American Mathematical Society, 136, (11), 3869-3874, 2008
Let X and X be compact Hausdorff spaces, and X , X be Banach lattices. Let X denote the Banach lattice of all continuous X -valued functions on X equipped with the pointwise ordering and the sup norm. We prove that if there exists a Riesz isomorphism X such that X is non-vanishing on X if and only if X is non-vanishing on X , then X is homeomorphic to X , and X is Riesz isomorphic to X . In this case, X can be written as a weighted composition operator: X , where X is a homeomorphism from X onto X , and X is a Riesz isomorphism from X onto X for every X in X . This generalizes some known results obtained recently.
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@inproceedings{jin2008a,
  title={A Banach-Stone theorem for Riesz isomorphisms of Banach lattices},
  author={Jin Chen, Zi Chen, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205947110829192},
  booktitle={Proceedings of the American Mathematical Society},
  volume={136},
  number={11},
  pages={3869-3874},
  year={2008},
}
Jin Chen, Zi Chen, and Ngai-Ching Wong. A Banach-Stone theorem for Riesz isomorphisms of Banach lattices. 2008. Vol. 136. In Proceedings of the American Mathematical Society. pp.3869-3874. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205947110829192.
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