The structure of compact disjointness preserving operators on continuous functions

@inproceedings{Lin2009TheSO,
  title={The structure of compact disjointness preserving operators on continuous functions},
  author={Ying-fen Lin and Ngai-Ching Wong},
  year={2009}
}
Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Σnδ ⊗hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator (© 2009… CONTINUE READING