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

MathSciNet review:
3003264

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Abstract | References | Similar Articles | Additional Information

Abstract: A pair of functions defined on a set with values in a vector space is said to be disjoint if at least one of the functions takes the value 0 at every point in . 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

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.