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

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.