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- Title
A Pre-adjoint Approach on Weighted Composition Operators Between Spaces of Lipschitz Functions.
- Authors
Abbar, Arafat; Coine, Clément; Petitjean, Colin
- Abstract
We consider weighted composition operators, that is operators of the type g ↦ w · g ∘ f , acting on spaces of Lipschitz functions. Bounded weighted composition operators, as well as some compact weighted composition operators, have been characterized quite recently. In this paper, we provide a different approach involving their pre-adjoint operators, namely the weighted Lipschitz operators acting on Lipschitz free spaces. This angle allows us to retrieve and sometimes improve some results from the literature. Notably, we obtain a distinct characterization of boundedness with a precise estimate of the norm. We also characterise injectivity, surjectivity, compactness and weak compactness in full generality.
- Subjects
LIPSCHITZ spaces; FUNCTION spaces; COMPOSITION operators; COMPACT operators; SURJECTIONS
- Publication
Results in Mathematics / Resultate der Mathematik, 2024, Vol 79, Issue 2, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-023-02115-x