Positivity

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Weakly compact weighted composition operators on spaces of Lipschitz functions

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Abstract

We prove that if X is a compact metric space and \({\text {lip}}(X,d)\) has the uniform separation property, then weakly compact weighted composition operators on spaces of Lipschitz functions \({\text {Lip}}(X,d)\) and \({\text {lip}}(X,d)\) are compact.

Keywords

Lipschitz algebra Weighted composition operator Compact operator Weakly compact operator 

Mathematics Subject Classification

Primary 47B38 Secondary 46E15 

Notes

Acknowledgements

The author would like to thank the referee for helpful comments to improve the paper.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsKharazmi UniversityTehranIran

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