This is an announcement for the paper "Biduality and density in Lipschitz function spaces" by A. Jimenez-Vargas, J.M. Sepulcre, and Moises Villegas-Vallecillos.

Abstract: 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 alternate 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 $(0,1)$.

Archive classification: math.FA

Mathematics Subject Classification: 46E10, 46E15, 46J10

Remarks: 7 pages

Submitted from: ajimenez@ual.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1407.7599

or

http://arXiv.org/abs/1407.7599