Unbounded disjointness preserving linear functionals

Lawrence G Brown Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43652

Monatshefte fr Mathematik, 141, (1), 21-32, 2004.1
Let <i>X</i> be a locally compact Hausdorff space and <i>C</i> <sub>0</sub>(<i>X</i>) the Banach space of continuous functions on <i>X</i> vanishing at infinity. In this paper, we shall study unbounded disjointness preserving linear functionals on <i>C</i> <sub>0</sub>(<i>X</i>). They arise from prime ideals of <i>C</i> <sub>0</sub>(<i>X</i>), and we translate it into the cozero set ideal setting. In particular, every unbounded disjointness preserving linear functional of <i>c</i> <sub>0</sub> can be constructed explicitly through an ultrafilter on complementary to a cozero set ideal. This ultrafilter method can be extended to produce many, but in general not all, such functionals on <i>C</i> <sub>0</sub>(<i>X</i>) for arbitrary <i>X</i>. We also make some remarks where <i>C</i> <sub>0</sub>(<i>X</i>) is replaced by a non-commutative C*-algebra.
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@inproceedings{lawrence2004unbounded,
  title={Unbounded disjointness preserving linear functionals},
  author={Lawrence G Brown, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205539999310181},
  booktitle={Monatshefte fr Mathematik},
  volume={141},
  number={1},
  pages={21-32},
  year={2004},
}
Lawrence G Brown, and Ngai-Ching Wong. Unbounded disjointness preserving linear functionals. 2004. Vol. 141. In Monatshefte fr Mathematik. pp.21-32. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020205539999310181.
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