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Characterizations of Disjointness preserving operators on vector-valued function spaces

Authors: Jyh-Shyang Jeang and Ying-Fen Lin
Journal: Proc. Amer. Math. Soc. 136 (2008), 947-954
MSC (2000): Primary 47B07, 47B38
Published electronically: November 23, 2007
MathSciNet review: 2361868
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Abstract: We characterize compact and completely continuous disjointness preserving linear operators on vector-valued continuous functions as follows: a disjointness preserving operator $ T : C_0(X, E) \to C_0(Y, F)$ is compact (resp. completely continuous) if and only if

$\displaystyle Tf = \sum_n \delta_{x_n} \otimes h_n (f)$   for all $\displaystyle f \in C_0(X,E),$    

where $ h_n : Y \to B(E,F)$ is continuous and vanishes at infinity in the uniform (resp. strong) operator topology, and $ h_n(y)$ is compact (resp. $ h_n$ is uniformly completely continuous).

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Additional Information

Jyh-Shyang Jeang
Affiliation: Department of Management Sciences, no. 1, Wei-Wu Rd., Military Academy, Fengshan Kaohsiung 830, Taiwan

Ying-Fen Lin
Affiliation: Department of Mathematics, National Hualien University of Education, Hua-Lien, 970, Taiwan

Keywords: Compact operators, completely continuous operators, disjointness preserving operators
Received by editor(s): August 4, 2006
Received by editor(s) in revised form: November 11, 2006
Published electronically: November 23, 2007
Additional Notes: The authors were partially supported by Taiwan NSC grants NSC94-2115-M-026-2116 and NSC94-2115-M-145-001.
The second author was supported by PIMS PDFs and was visiting the University of Alberta when this work was completed
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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