The structure of compact disjointness preserving operators on continuous functions

Ying-Fen Lin, N.-C. Wong

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 = Snd ?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
Original languageEnglish
Pages (from-to)1009-1021
Number of pages13
JournalMathematische Nachrichten
Volume282
Issue number7
DOIs
Publication statusPublished - 01 Jul 2009

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