Artigo
Isomorphisms between spaces of Lipschitz functions
Fecha
2019Registro en:
10.1016/j.jfa.2019.02.003
Autor
Candido, Leandro [UNIFESP]
Cuth, Marek
Doucha, Michal
Institución
Resumen
We develop tools for proving isomorphisms of normed spaces
of Lipschitz functions over various doubling metric spaces and Banach
spaces. In particular, we show that Lip0(Zd) ≃ Lip0(Rd), for all d ∈ N.
More generally, we e.g. show that Lip0(Γ) ≃ Lip0(G), where Γ is from
a large class of finitely generated nilpotent groups and G is its Mal’cev
closure; or that Lip0(ℓp) ≃ Lip0(Lp), for all 1 ≤ p < ∞.
We leave a large area for further possible research.