TY - JOUR

T1 - The structure of compact disjointness preserving operators on continuous functions

AU - Lin, Ying-Fen

AU - Wong, N.-C.

PY - 2009/7/1

Y1 - 2009/7/1

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-76649097319&md5=3f39ef2b700a77927aed8401d6c33f00

U2 - 10.1002/mana.200610786

DO - 10.1002/mana.200610786

M3 - Article

AN - SCOPUS:76649097319

VL - 282

SP - 1009

EP - 1021

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 7

ER -