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COMPACT WEIGHTED COMPOSITION OPERATORS BETWEEN $L^{p}$-SPACES

Part of: Special classes of linear operators Classical measure theory

Published online by Cambridge University Press:  16 January 2020

CHING-ON LO Open the ORCID record for CHING-ON LO [Opens in a new window]  and
ANTHONY WAI-KEUNG LOH Open the ORCID record for ANTHONY WAI-KEUNG LOH [Opens in a new window]
CHING-ON LO*
Affiliation:
Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong email [email protected]
ANTHONY WAI-KEUNG LOH
Affiliation:
Division of Science, Engineering and Health Studies, College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong email [email protected]
*
✉[email protected]
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Abstract

We provide complete characterisations for the compactness of weighted composition operators between two distinct $L^{p}$-spaces, where $1\leq p\leq \infty$. As a corollary, when the underlying measure space is nonatomic, the only compact weighted composition map between $L^{p}$-spaces is the zero operator.

Keywords

weighted composition operatorsLebesgue spacescompact operators

MSC classification

Primary: 47B33: Composition operators
Secondary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 151 - 161
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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References

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