A Banach-Stone type Theorem for invariant metric groups

Mohammed Bachir (1)

1 Equations d'evolution

Given an invariant metric group $(X,d)$, we prove that the set $Lip^1_+(X)$ of all nonnegative and $1$-Lipschitz maps on $(X,d)$ endowed with the inf-convolution structure is a monoid which completely determine the group completion of $(X,d)$. This gives a Banach-Stone type theorem for the inf-convolution structure in the group framework.

Keywords: group and monoid structure.; isometries; Banach-Stone theorem; $1$-Lipschitz functions; inf-convolution

Domains: Functional Analysis [math.FA]

Mohammed Bachir. A Banach-Stone type Theorem for invariant metric groups. Topology and its Applications, 2016. ⟨hal-01333611⟩