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Fredholm Weighted Composition Operators Between Lipschitz Algebras

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Abstract

Let X and Y be (not necessarily compact) metric spaces. We provide a complete description of Fredholm weighted composition operators between Lipschitz algebras \(\textrm{Lip}_\alpha (X)\) and \(\textrm{Lip}_\alpha (Y)\) for \(0<\alpha \le 1\). All results and some more hold when such operators are between little Lipschitz algebras \(\textrm{lip}_\alpha (X)\) and \(\textrm{lip}_\alpha (Y)\) with \(0<\alpha <1\). As an application, we characterize Fredholm multiplication operators on little Lipschitz algebras and show that the Fredholm index of such operators is zero.

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Acknowledgements

The authors would like to thank the referee for his/her useful comments and suggestions.

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  1. Department of Mathematics, Kharazmi University, 50, Taleghani Ave., Tehran, 15618, Iran

    Hakimeh Mahyar & Sajjad Mohammadi

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  1. Hakimeh Mahyar
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  2. Sajjad Mohammadi
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Correspondence to Hakimeh Mahyar.

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Mahyar, H., Mohammadi, S. Fredholm Weighted Composition Operators Between Lipschitz Algebras. Results Math 78, 174 (2023). https://doi.org/10.1007/s00025-023-01956-w

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