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 $α \in (0,1)$.