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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Compact and weakly compact disjointness preserving operators on spaces of differentiable functions


Authors: Denny H. Leung and Ya-shu Wang
Journal: Trans. Amer. Math. Soc. 365 (2013), 1251-1276
MSC (2010): Primary 46E40, 46E50, 47B33, 47B38
Published electronically: November 27, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: A pair of functions defined on a set $ X$ with values in a vector space $ E$ is said to be disjoint if at least one of the functions takes the value 0 at every point in $ X$. An operator acting between vector-valued function spaces is disjointness preserving if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions.


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Additional Information

Denny H. Leung
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076
Email: matlhh@nus.edu.sg

Ya-shu Wang
Affiliation: Department of Mathematics, National Central University, Chungli 32054, Taiwan, Republic of China
Address at time of publication: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
Email: wangys@mx.math.ncu.edu.tw, yashu@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05831-4
PII: S 0002-9947(2012)05831-4
Keywords: Disjointness preserving operators, spaces of vector-valued differentiable functions, compact and weakly compact operators.
Received by editor(s): March 11, 2011
Published electronically: November 27, 2012
Additional Notes: The research of the first author was partially supported by AcRF project no. R-146-000-157-112
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.