TY - JOUR AU - Jiménez-Vargas, A. AU - Sepulcre, J. M. AU - Villegas-Vallecillos, M. PY - 2017/09/22 Y2 - 2024/03/29 TI - Biduality and density in Lipschitz function spaces JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 121 IS - 1 SE - Articles DO - 10.7146/math.scand.a-25987 UR - https://www.mscand.dk/article/view/25987 SP - 92-100 AB - <p>For pointed compact metric spaces $(X,d)$, we address the biduality problem as to when the space of Lipschitz functions $\mathrm{Lip}_0 (X,d)$ is isometrically isomorphic to the bidual of the space of little Lipschitz functions $\mathrm{lip}_0 (X,d)$, and show that this is the case whenever the closed unit ball of $\mathrm{lip}_0 (X,d)$ is dense in the closed unit ball of $\mathrm{Lip}_0 (X,d)$ 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 $\mathrm{Lip}_0 (X,d^\alpha )$ is isometrically isomorphic to $\mathrm{lip}_0 (X,d^\alpha )^{**}$ for any $\alpha \in (0,1)$.</p> ER -