A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces
Year: 2025
Type: article
Abstract: Fix a metric space M and let Lip0(M) be the Banach space of complex-valued Lipschitz functions defined on M. A weighted composition operator on Lip0(M) is an operator of the kind wCf:g↦w⋅g∘f, where w:M→C and f:M→M are any maps. When such an operator is bounded, it is actually the adjoint operator of a so-called weighted Lipschitz operator wˆf acting on the Lipschitz-free space F(M). In this note, we study the spectrum of such operators, with a special emphasis when they are compact. Notably, we obtain a precise description in the non-weighted w≡1 case: the spectrum is finite and made of roots of unity.
Source: Journal of Operator Theory
Authors: Arafat Abbar, Clement Coine, Colin Petitjean
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4414580900
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