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(alpha)) with alpha is an element of (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. (C) 2010 Elsevier Inc. All rights reserved.