Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions

Abstract

We show that the isometry groups of Lip(X,d) and lip(X,d^α) with α ∈ (0, 1), for a compact metric space (X,d), are algebraically reflexive. We also prove that the sets of isometric reflections and generalized bi-circular projections on such spaces are algebraically reflexive. In order to achieve this, we characterize generalized bi-circular projections on these spaces.