Albiac Alesanco, Fernando JoséAnsorena, José L.Cúth, MarekDoucha, Michal2022-08-312022-08-312021Albiac, F.; Ansorena, J. L.; Cuth, M.; Doucha, M.. (2021). Lipschitz algebras and Lipschitz-Free spaces over unbounded metric spaces. International Mathematics Research Notices .1073-792810.1093/imrn/rnab193https://academica-e.unavarra.es/handle/2454/43908We investigate a way to turn an arbitrary (usually, unbounded) metric space M into a bounded metric space B in such a way that the corresponding Lipschitz-free spaces F(M) and F(B) are isomorphic. The construction we provide is functorial in a weak sense and has the advantage of being explicit. Apart from its intrinsic theoretical interest, it has many applications in that it allows to transfer many arguments valid for Lipschitz-free spaces over bounded spaces to Lipschitz-free spaces over unbounded spaces. Furthermore, we show that with a slightly modified pointwise multiplication, the space Lip(0)(M) of scalar-valued Lipschitz functions vanishing at zero over any (unbounded) pointed metric space is a Banach algebra with its canonical Lipschitz norm.application/pdfeng© The Author(s) 2021. Published by Oxford University Press. All rights reserved.Lipschitz-free spacesLipschitz algebrasUnbounded spacesinfo:eu-repo/semantics/article2022-08-31info:eu-repo/semantics/openAccess