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.

Keywords: auto-continuity, Fredholm operators, disjointness preserving operators, weighted composition operators

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