Biduality and density in Lipschitz function spaces - Jiménez-Vargas, A.; Sepulcre, J. M.; Villegas-Vallecillos, M. (Mathematica Scandinavica, 2017)
For pointed compact metric spaces (X,d), we address the biduality problem as to when the space of Lipschitz functions Lip_0 (X,d) is isometrically isomorphic to the bidual of the space of little Lipschitz functions lip_0 (X,d), and show that this is the case whenever the closed unit ball of lip_0 (X,d) is dense in the closed unit ball of Lip_0 (X,d) with respect to the topology of pointwise convergence. Then we apply our density criterion to prove in an alternative way the real version of a classical result which asserts that Lip_0 (X,d^α ) is isometrically isomorphic to lip_0 (X,d^α )^** for any α (0,1).