Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 61-75.

Disjointness preserving Fredholm linear operators of

$C_0(X)$

Authors: Jyh-Shyang Jeang (1) and Ngai-Ching Wong (2)
Author institution: (1) Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
(2) Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, Republic of China

Summary: Let

$X$ and

$Y$ be locally compact Hausdorff spaces. We give a full description of disjointness preserving Fredholm linear operators

$T$ from

$C_0(X)$ into

$C_0(Y)$ , and show that

$T$ is continuous if either

$Y$ contains no isolated point or

$T$ has closed range. Our task is achieved by writing

$T$ as a weighted composition operator

$Tf=h\cdot f\circ\vp$ . Through the relative homeomorphism

$\vp$ , the structure of the range space of

$T$ can be completely analyzed, and

$X$ and

$Y$ ar e homeomorphic after removing finite subsets.

Contents Full-Text PDF